I wrote out a nice guide, but then my document expired. I will work on updating this. Dont take builds other than the first one seriously, I have learned a lot since then.

Long story short.
Early
Faerie Charm and Cloth Armor can help you a lot, even before you finish stalkers blade. Hunter's Potion can help sustain if you have extra gold early.

My 1st Clear Order is [ Gromp (w/ smite nad leash)-> Wolves -> Blue (w/ smite)-> back if im dying ->Birds ->red (w/ smite) - Krugs (w/ smite)- Scuttle (w/ krug buff stun)

I am tempted to try to start blue, because when i do this, i end up being nearly dead after blue.

It is mildly hard to kill scuttles without krug buff (or quality Q skill), but it is a good place to try to fight the other jungler because you can ping and your allies may come to aid you.

Rush
Stalker's Blade - Runic Echoes
Get Tear of the Goddess if you have not once you get echoes. I usually get this before runic echoes, without it, you cannot gank at all, you run out of mana very quickly when you try, and this solves that issue.
Get Rylai's Crystal Scepter and Sorcerer's Shoes

Build appropriately. Often one should build something situational before completing Archangel's Staff because it might not be the safest choice. The Tear is more than enough mana once it gets charged, and the blue buff is enough sustain. Don't spend too much time in river, because the Jungle Mana Regen doesn't work there, and there are no minions for you to kill.

Common

Liandry's Anguish - This is good if the enemy team doesnt have a lot of initiate that can lock you down. You kite them with E when they try to initiate, and they cannot root/catch you this is good damage.

Archangel's Staff - Quality common upgrade. Very Nice once tear has 750/750, but before the it is not as great.

Rabadon's Deathcap - Expensive, but a huge DPS Boost. This can be good if you are getting fed with low threats. (Main threats are assasins, CC, and champs with slow and chase)

Void Staff- Counter enemies that stack Magic Resist.


Defensive

Zhonya's Hourglass - This is good AP, and it can save your life if you get caught in a team fight (not so much if caught alone). Its also good for ultimates like Fizz or Zed that you can time to avoid.

Abyssal Mask - This is good against Melee Range Magic assasins like Kassadin, Nidalee, and Akali, who will be in range of this item and your E. The range of E is slightly larger than the range of this item though.

Situtaional

Mercury's Treads- If you face a lot of roots/ stuns /silences, but you would might be able to survive them.

Boots of Swiftness- If you face a lot of chase and slows. These can help you stay alive.

Frost Queen's Claim - This item is stupid OP at the moment. The ghosts give you all the initiate you need to catch somebody in your slow field and this will often ensure their death.

Morellonomicon - When you face Lifesteal / Healing / Regen based champs that are sustaining through your fights. This can help. CDR is nice too.

Lich Bane- Might seem weird, but it is good for split pushing and gives you even more Move Speed which is great for staying alive. CDR is nice too.

Will of the Ancients - This can give you good sustain and regen by eating big waves of minions with E + Q. It might not be amazing regen, but if the enemy team lacks burst it can keep you in the fight.

Thornmail - Against fed and dangerous auto attack based champs like Rengar or Yi, this can help you survive a bit, and damage them enough to maybe pick them off with your passive if you get caught. It may deter them from isolating you if you have a good bit of health as well. When cloth armor will not do and your getting caught, this can be prio'd alongside Rylai, getting the thick armor.

Banshee's Veil- This will stop a Nidalee Spear or a Veigar spell, it can be useful, but it has along cooldown and no offensive stats.

Quicksilver Sash - This will save you from Malzahar ultimate, fizz ultimate, stuns, mushrooms, and plenty of stuff. This shouldnt be upgraded unless you have full build. This is the only defensive item without and offensive stats that I would take early as the 3rd item.


Tracker's Knife - The ability to seal movespeed is essential against enemies that can lock you down or easily stay in range of you. Stalker's slow is the only real escape you have, but if your team needs wards, this can be switched to after Rylai's.


Dubious
Rod of Ages - I Do not like this item because you have to rush it first in order for it to be very good, and you can get health/mana from tear and rylai. It doesn't provide any real utility when compared to Rylai which helps you secure many, many kills. Regardless of this being a good all around item when starting mid, i don't feel it is viable for the jungle.

Warmog's Armor - This can be an option if you get up to 2200 total HP. It doesn't seem great because you will often get caught more than you will be able to escape.

Note: Rylai alone will not get you to 2200 HP, even at level 18. only to 2191. If you want to run Warmog, I would suggest taking a few scaling HP runes.


I have to go, but i will try to make this one look pretty some other time.

Pen for days.
I take 1 Flat Armor for safety in early clear. I take 2 Mobility quints because this allows you to win a foot race and often this will save your life.

Take flat armor over scaling to give you better early Clears.

Move speed because you gotta go fast or you are gauranteed to get caught. Every little bit helps.

I personally run 6x Scaling CDR blues, but this makes you suceptible to magic damage. I just run this on all wizards, it is likely not ideal, as CDR really only helps with Wall and Ultimate on Karthus.

*New- Pre-season 7* I have tried this since the new jungle changes. Sadly, it is a bit harder to clear now. This is why I suggest a few scaling Mana Regen runes, because once blue buff falls off, you are often low or out of mana when the tear has low stacks early in the game. Against aggressive junglers your team can fall behind because of the weakness of your ganks, and the scaling Mana regen is helpful in the middle levels when you might not have blue, as it surpasses standard mana regen at level six.

Doing the Deed/url]

This is a semi-pro guide; it loses strength in pro leagues because your susceptible to other traditional junlgers. Feel free to try it out if you are pro, but you are vulnerable.

I had never played karthas before making this guide. I learned he is a very difficult hero to play, and it takes a bit of effort to jungle effectively.

Karthas does not like to use his auto, so you should be spamming rightclick on monsters as well as Q when mousing over them. This build has a slow build and you are nearly worthless for a long time early as well as very fragile, but karthas can jungle effectively with runeglaive seekers and swiftness.





I have played build one and it works, but I am bad at karthas, but with some skill it could be somewhat applicable; he is a very difficult champ to play.

Played this (6/28/15) and got S-.

Early Game

You die without armor.
Machete gives you some ability to not die.
Get both even if you have to go back after the leash kill.

Purchase Order
1. Ranger's Trailblazer
2. Cloth Armor
3. Boots and Sapphire Crystal
4. Enchantment: Runeglaive (This can be taken before boots if you want to rush it)
5. Seeker's Armguard
6. Boots of Swiftness
7. Needlessly Large Rod/
~ Spectre's Cowl / Boots of Swiftness - Alacrity
8. Zhonya's Hourglass
9. Needlessly Large Rod or Blasting Wand / Spirit Visage
10. Rabadon's Deathcap
11. Void Staff


Mid Game

Ranger Blazer is the only thing keeping you in the jungle and not on the bench; aka sitting at the fountain.

Runeglaive is that wizard magic.

Arm-guard is the armor you want, and the AP is nice.

Boots of Swiftness- This is key for escaping ganks, running from lost team fights, being able to arrive at ganks fast enough, going from jungle to jungle and from base to jungle.

Boots - Alacrity- Move speed is everything, when you have this, it takes another hero with swiftness and alacrity just to keep up with you if you have not been slowed, so it is much more likely that you will escape.


End Game

Rabadon- This is the clasic wizard hat. It is good for wizards.

Hourglass- This is the only think arm-gaurd builds into that i know of.
Merc Treads HG - You're likely going back to base because you've got a heart of glass. This will help you get back into the jungle. You also don't have any MR so stay classy.


Visage- This gives you MR, Regen, and Health, which will help you stay alive, but the lack of AP makes your wizardry a bit less powerful. This can be replaced with mallet for an even more impactful auto attack if you do not need MR in case the enemy wizard threat is not impactful.

Without MR you can easily be one shot by casters.

Void- Take this if you are a strong independent woman that don't need no MR. You deal magic damage, and this helps you get past much more of the enemy's MR than Abyssal. This is the common 6th item as yo have no maigc pen. This will make you very fragile against wizards and thats not ideal for a jungler as you often go into fights with half health or something like that cause you're a wild animal from the woods. This can be replaced by an alternate item if the enemy does not have a deep magic threat. (I suggest taking this over Nashor because the CDR is meaningless when your spells end up doing little damage.)

Athene's Unholy Grail - This is great because it gives you bonus MR. The real reason is for the mana regen. This build has **** regen without it, but only when your outside of the jungle. While jungling mana is fine and so long as you can escape to the jungle to regain mana you should be ok. The problem with lacking mana is when assaulting the enemy base. The cooldown reduction is also great for ultimate. This would be alternate number 1 over void staff.

Void staff is going to be the main item you want an alternate for. The armgaurd in Zhonas is key early on, and Visage is the only source of both MR and Health in this build.

Abyssal Mask- You can take this instead of Visage if you've got enough health to stay alive somehow, and you still want some real MR because another wizard is breaking you with his stone cold stunner. The health from Visage is helpful, but more AP is always good in actual team fights rather than jungling.


Frozen Mallet- This gives you an excuse to get red stones because you're dead more or less and don't have much health. This also gives you some slow when you use your auto. This build has much focus on the impact of the auto, regardless of lacking much AD. (If you take this you will want a replacement MR item like abyssal instead of void for 6th item. Karthus attacks faster than 1.5 sec per attack without any attack speed, so keeping this applied should be possible, especially with swift boots. This can be helpful if enemies avoid your wall, or you want to slow them down between casts of wall. This is not a highly viable item though)

Sorcerer's Shoes- These can be big money for killing those lacking the MR. These are not ideal for this build though, because Jungle Karthus wants to move through the jungle quickly, and above all be able to run away from team fights that have turned into the favor of the enemy. Being snared or at all will likely kill you in most situations, so tenacity will not help you as much. The idea with swiftness it to avoid being snared in the first place.

Mercury's Treads - This if you need tenacity. When Lacking the speed of swift+ alacrity, the tenacity will do litlte or nothing to save your life in a bind. The logic behind swiftness is to not get caught in the bind in the first place.

Homeguard- This is the offensive enchant if you find you are not going back to the base very often to heal. This is more speed in the jungle and some more maneuverability within fights.



Nashor's Tooth- If somehow you've got to have some threat on your auto-attack because you've got that spellblade. Karthus attacks faster than 1.5 sec without any attack speed, so this is not needed, as you can get off the spellblade proc each time without a problem. AP is nice and CD reduction is nice. (This is likely not as good as athenes)

Q is your main blast. This is nice in the jungle. It deals double damage once you kill the minis.

W is for peeling and securing kills by slowing runners. Even one rank should be enough for you to escape. Having points in this is easily more useful than E, this build does not have the mana to sustain E for very long, so having a high quality slow to help secure kills and help you land Q on enemies is nice. This spell does nothing in the jungle.

E is terrible in the jungle if toggled on, it burns mana very fast and it is designed to kill 6 or 7 mobs that come with a wave in a lane. Only use this active when you have high mana and low health where you will die without extra dps, but you will not run out of mana from using it. This happens sometimes in early clears of jungle. Keep this toggled off and you get MP per kill which is nice.

R is great for a cowardly fighter like yourself to help your allies secure kills. Your fragile but this gives you the ability to do some damage anywhere on the map, as well as secure kills on runners. This can be used in the jungle so keep an eye on your allies trades so you can time this to help secure a kill.

The order is not important, but Q is the priority, and you get the most value per point in E with only one point, but it is also good for the minis in the jungle.

Stay alive with those defense points, makes it a bit tougher to lock you down long enough to kill you, which can easily happen instantly to these points may be worthless.

Offense points. These are nice, look at the emphasis on wizard magic. That pinnacle Arcane Blade will put some flavor on your auto.

Defense is key. Dying is bad. This is not meant to be the main wizard threat, so staying alive to provide the dual threat of support and kill secures as well as some decent damage is nice.

The flat armor is the best here. Late game you should not be taking hits. You start the game with the flat armor and this means you take reduced damage from jungle mobs which is key.

Cooldown Reduction because blasting that ultimate is essential. This also lowers cooldown on wall which is quality.

Magic Penetration because it is quality.

I am not an internet wizard. But this is a guide on the internet on how to be a wandering wizard of the forest that is published on the internet. Results may vary.

Spam Q and Right Click on the Mob you Are killing.

It is essential to aim Q in a way that it only hits one of the minis for the creeps that have them. This causes it to do double damage, which means that it kills the mini twice as fast and this means it does half the damage to you. Karthus is very fragile early on. (This is not needed on the small birds sometimes, especially after ranger smite, as you can kill them with one or two Q blasts that hit all 3 of them. This is very key on the Rock man, Red/Blue, and Wolves, as you take less damage. This is not hard to master.)

Using E is very ineffective in the early game and is still very mana hungry at all points in the game. Do not use it when jungling, use it if you are pushing a lane or clearing it back when covering for someone who goes back.

With Runeglaive you become an effective jungle but still very fragile. The runeglaive gives you unlimited mana.

It is easy to have the ultimate cancel because of moving mistakes. Dont try to use it during a fight if there is any chance the enemy can stun you or kill you; it has a long cooldown and this wastes it entirely. It is not very strong, especially without AP (this build has little ap sadly) but it can still help team fights and be cast from a safe spot in the jungle, just keep an eye on when enemies are in a position where they could be caught with low health <35% or so, and have a good deal of distance for them that they would need to retreat, and you also have an ally in good position to attempt to take them down.

I have caught many runners with R. These are quality kills and they help you get your build full much quicker. Keep an eye on team fights and see when/if someone has low health or runs away.

Karthas is a very good laning guy. Keep this in mind and be sure to help clear lanes and push lanes if you can.

Q is the only thing doing anything in the jungle. E will cause you to go OOM very very quickly, especially without runeglaive.

With runeglaive E can be used sparingly. Use E in an emergency situation when you could die if you do not have added dps, and you also still have a lot of mana.

I am bad at aiming W, it will always be a wall in the direction you cast it, and often times this means it will be sideways or something when attempting to gank. Karthus is bad at ganks with no real stuns or slows, no bonus movement, a difficult control spell, Q is difficult to aim, and overall he is very hard to play, so keep that in mind.

Pros
Fast Jungle Clear Eventually (Once you have runeglaive. It is reasonable without runeglaive if you can skillshot Q to hit one mini at a time, but you take a good bit of damage early on; hence the armguard.)
Jungle is amazing mana battery
Jungle is a safe place to requiem. This is key to finish off runners and get assists in order to fuel the build.
Decent Peel
Decent Lane Pushing (not towers so much)
Mobile and Threatening with Swiftness, W, Q and R
Good Slow to secure kills.
Q is great against large groups of enemies if they are focusing on another champ that can stay alive and keep them clumped together.
Ultimate can secure kills on runners with low health from anywhere on the map.


Cons
Slow Build / Expensive without kills and assists (but what build isn't)

Fragile Early, to both champs and monsters.

Bad Damage input in Team Fights Early Game (And all game w/o skill with landing Q)/ Ganks
The damage input becomes reasonable with Skill of course, and AP. If you don't land Q you don't do any damage.

Susceptible to ganks (w/o swiftness; run away is far better than dying; use wall to avoid these)

Has to back very often, mainly in early game. I can get a reliable clear of gromp (w/ leash and smite), then wolves, then smite on turtle (turtle is difficult to kill without smite, it moves around rather than stands still like normal monsters, so it takes skill to even land your Q, your main source of damage). This backing issue is not usually a problem with even minimal gear, just bring potions, health more so than mana.


E is very mana hungry

Very Skill Based Champ. If you have trouble landing Q reliably you will not do well. You must aim it to where the enemy will be in about a half a second, so aim it in the direction that they are moving and they will likely walk over it if you have done it right.

Just showing up and throwing the wall out is enough to scare off some people. You may not be a damage threat early but people don't know this. You are just a reason for people not to chase kills, and if you can land Q effectively you become a real threat, but this is difficult.

Staying alive is key. Swiftness is really the only way to do this. This keeps you from being ganked and chased down 90% of the time, don't try to fight people solo unless you're built. If you're built and they have like 30% health or lower it is possible to hit E if they are melee and be lucky landing Q to score a kill; the real kills come from killing runners with R.

Try to peel for people when you can, show up in lanes sometimes. It is dangerous to try to get into the fight or in range to use E, but it can deter people from chasing an ally with low health if your also good at landing Q.

Landing Q takes practice but it is very strong if you can do it.

Landing the Wall can secure some ganks. It doesnt matter how straight or wall-like it is, if you can land it directly on the enemy it is solid. It is also good escape and great for protecting allies, swiftness helps a lot in getting to team fights.

2nd Build - This is for slow and heavy damage. This build is fragile.
3rd build- This is for slow and some defense. (E is worthless without defense)

4th build- This can take more damage, but the output is far lower.
6th item for 4th build. Take what you want. AP / Penetration / Mana regen / Armor (against strong AD carry) / MR against strong AP carry.

4th build would be used to support and peel for people more than secure kills.

Speed Build kind of a joke, but if you have teamwork you can help secure

Need for speed build; i dont think you can trigger two spellblades, even if one is on cooldown, but maybe you can, idk. If not, you can replace it with talisman or scimitar

I have yet to try this one. Results vary the way i play karthus in the original build. This is a new one.

Lessons learned. You realy want [tear of the goddess] because you get % mana back from runeglaive.

Alt Items- These Are for Seraph. If you dont have time to max another tear you might want one of these. You really want seraph though. It is easy to max the first tear as karthus because your spell CD is so low.
Gunblade- This is damage and AP. You push towers and so this is solid stuff. The spellvamp is only good if you can hit one monster at a time in the jungle with Q.

Zeyphr- Attack speed, cooldown reduction and move speed and tenacity. Everything you want.
Heart- If there is AD Carry you are soft like an AD carry, but you have no real scaling with AD.
Rod- Mana is good. Health is good.
Angel - Good All around item for defense.
Purchase Order

Jungle very much. If you are in a team fight and the enemies are not around, spam Q regardless, you want to get them tear charges.