Hi! I am Sam I Yam, formerly Sambu1, a Silver scrublord on NA who likes to have some fun playing unconventional picks in various roles. Support Karthus is something I have been playing around with for a while now, and although not being "hidden OP" or anything of the like, I do believe it is a somewhat viable pick in the bottom lane. At least in Silver.

Pros

• Spam-able poke
• Great zoning potential
• Long range on Lay Waste
• High sustained damage
• Late-game carry potential

Cons

• Squishy early
• Very immobile
• Item dependent
• Can run out of mana easily
• Only crowd control is a weak slow

Quints:
Greater Quintessence of Ability Power x3: Great for poke in lane and general early-game damage. All-around best quints on support Karthus.
Greater Quintessence of Magic Penetration x3: Karthus has very high base damage compared to his AP ratios, so some people opt to go for magic penetration over ap. This does, however, lower your early-game damage and, in my opinion, inferior to flat AP quints.
Greater Quintessence of Gold x3: Help achieve the end game build much faster, but at the expense of much of your early-game power. Pretty much unusable. However, if you can pull it off, it feels amazing.

Marks:
Greater Mark of Magic Penetration x9: Generally the best offensive marks for mages. All other offensive marks are either inefficient or pointless on Karthus.

Seals:
Greater Seal of Armor x9: In the bottom lane you will be facing mostly physical damage, so armor seals are generally the best choice.
Greater Seal of Health x9: Another defensive option, heath seals are good if you fear poke from enemy supports. Supports for the most part deal magic damage and armor will not help you mitigate it. Health seals allow you to take more hits from both bottom laners rather than focusing on only the ADC.
Greater Seal of Armor x4 + Greater Seal of Health x5: A common compromise between armor and health seals.
Greater Seal of Gold x9: See gold quints.

Glyphs:
Greater Glyph of Scaling Ability Power x9: Great scaling into the mid and late game. These are my preference for glyphs as I generally don't get a chance to buy any significant AP until at least mid game.
Greater Glyph of Ability Power x9: Flat AP allows for even better poke in the early game. The choice between flat and scaling AP is mostly up to preference.
Greater Glyph of Magic Penetration x9: Again, Karthus has great base damage and relatively low AP ratios. Choosing there does hit some of your early poke in favor of late-game damage.


Honestly, if you think you can play safe enough, GP10 runes are hilarious and help achieve your "late game fantasy".

Offense: 13 points
Sorcery: Cooldown reduction is good on Karthus for more ultimates.
Expose Weakness : Amplified damage for your whole team once you hit someone. Keep in mind that "allied champions" includes yourself. Great, especially in a duo lane where you can maximize the benefits of it early and often.
Mental Force : Put all 3 points in here. Used mostly to get to the next tier of masteries.
Arcane Mastery: The reason you put those points in Mental Force . Great single-point mastery that boosts your early-game damage.
Executioner : Damage amplification on low-HP targets. Great for securing kills with your ultimate. Take all 3 points in this.
Dangerous Game : This saves lives

Defence: 0 points
Because you aren't a p*ssy.

Utility: 17 points
Fleet of Foot: You are slow. Really slow. This can fix it a bit. Put 3 points in it.
Meditation : Before you get your tear stacking, you use up your mana very quickly. Do what you can to remedy that by putting 3 points into this. The change from mana regen to a flat 75 mana (with 3 points in it) is a buff in the very early game (levels 1-4) but soon after that the mana regen would have provided more mana.
Summoner's Insight : As Karthus, you have very little mobility and your only escape is flash. 3 points in this takes 30 seconds off its cooldown.
Alchemist : Karthus is very squishy. The extended duration on potions allows you to sustain in lane and allows you to base less frequently.
Culinary Master : The biscuits give you instant health and mana in addition to the normal potion health over time. More sustain as well as potential clutch potion chugging vs ignite and other damage over time is worth putting a point into.
Greed : As a support, you need to take everything you can get, especially on someone as item-reliant as Karthus.
Scavenger : Even more gold.
Wealth : This extra 40 starting gold allows you to start with an extra potion or -1 potion and a ward. Very worth taking. In most cases you want to get the extra potion over the ward.
Bandit : More gold. Keep in mind it does not proc off of abilities but only auto-attacks. This is the least important mastery and the point can be put somewhere else if you prefer.

Starting Items
Start with a Spellthief's Edge and a mix of Health Potions and Mana Potions. You can even start with a Vision Ward for extra early vision. I prefer to go with 3 Health Potions and 1 Mana Potion against most match-ups as Karthus is a squishy target that needs lots of health sustain to get through early poke. Replacing a Health Potion for another Mana Potion is fine if you plan to go for more aggressive poking.

Core Items
Frost Queen's Claim: I normally choose not to upgrade Spellthief's Edge. Although the upgrades are not horrible in of themselves, they delay the purchase of more valuable items. Frost Queen's Claim is a good item, and gold efficient at that, but in an already expensive core for a support the extra stats and GP10 don't always cut it. Can be bought if you are behind.
Sightstone: At least in Silver, I have been able to get away with not buying this item. Instead, immediately upgrade your Stealth Ward into a Greater Stealth Totem at level 9. This should allow you to keep 2 to 3 wards on the map at all times. However, sometimes this is not enough and a Sightstone on your first back can light up the map.
Tear of the Goddess: Try to get this as early as possible to get it stacking. Karthus burns through mana very fast with this Defile so stacking mana is very good on him.
Archangel's Staff: The upgraded version of Tear of the Goddess. Don't rush this item. Sitting on a fully stacked tear is perfectly fine if you have not completed the other core items.
Zhonya's Hourglass: A great item on Karthus. All of the stats on this item are used to great effect on Karthus and the active is amazing. Make sure to have Defile on when you use the active as it will continue to work in stasis. The active on this item is useful for making plays in teamfights by baiting, switching focus, and/or avoiding damage.
Ionian Boots of Lucidity: Although the magic penetration from Sorcerer's Shoes is very useful and helps your damage output immensely, the 15% CDR from Ionian Boots of Lucidity allows you to help your team more often with global pressure from your ultimate. Either boot choice is fine, however I definitely prefer Ionian Boots of Lucidity.

Other Items
Once you get your core items, you should start to try to eclipse your mid laner as a damage source. Start getting some farm from the jungle and lanes as your team transitions into the mid game. Still help your other carries get fed and farmed, but also think about yourself.
Rylai's Crystal Scepter: Health is a very good stat on Karthus as he will be closer to the front line than other mages. The slow is very useful to help land more Lay Wastes and adds to your general utility.
Rod of Ages: If you manage to get some early kills and can afford to finish this item before ~20 minutes, preferably earlier, you can replace Rylai's Crystal Scepter with this. If you feel the need to, you can opt to build both items to stay in the fight much longer.
Rabadon's Deathcap: Pure AP, and lots of it. A very offensive item that will boost your damage immensely once purchased.
Void Staff: AP and percent magic penetration. In most cases this item will actually increase your damage more than Rabadon's Deathcap because of Karthus's relatively low AP ratios and high base damages. Even against targets with low magic resistance Void Staff will often do more damage than Rabadon's Deathcap.
Abyssal Mask: Generally the best item for magic resistance on Karthus. The AP and aoe magic resistance reduction do well with Karthus's kit and it gives Karthus a sizable amount of MR for himself.
Luden's Tempest: In the very late stages of the game you may opt to swap out your boots for this for even more damage. It gives 7% movespeed, which, when combined with the third dragon buff, is enough to get around with. Very situational whether you chose to go for the extra damage because if you cannot catch up to your enemies it just won't matter.

Honestly, I'm no expert Karthus player. Look at some mid lane guides for more item insight.

Passive: Death Defied
Death Defied is a core part of Karthus's gameplay. When Karthus dies, he enters a "spirit form" where he can cast spells without mana costs for 7 seconds. He cannot be targeted or interrupted for this time. This allows you to charge into a fight, die, and still do damage. Don't go in trying to die (that's feeding) but keep in mind that you will still be able to fight after death. During this time, your E, Defile will automatically turn on (unless you haven't put any points into the skill) so don't bother trying to spam it like I did when I first played Karthus.

Q: Lay Waste
Max this first for early poke. It has long range and a very low cooldown that can be used to zone the enemy ADC from minions and even experience. The one second cooldown allows you to spam this as much as you want. Try to use this spell as much as you can, but keep an eye on your mana pool. Keep in mind that this spell does double damage when it hits just one target. For the purpose of items, such as Rylai's Crystal Scepter, it also acts as a single target spell when only one target is hit. This means it will apply the full 35% slow on Rylai's Crystal Scepter rather than the aoe 15% slow when it hits one target.

W: Wall of Pain
Max this spell last. Wall of Pain creates a wall that slows all enemies hit for 5 seconds. It also applies a debuff to them for the same duration that reduces their magic resistance by 15%. Putting levels in this spell increases the width of the wall and the slow strength, but not the MR reduction. This is Karthus's only form of crowd control and is on a somewhat long cooldown. In fights, make sure to land this on as many people as possible reduce the enemy's magic resistance and increase your team's magic damage against as many targets as possible.

E: Defile
Max this spell second. Defile is an aoe, damage-over-time, toggle ability. At early ranks this spell does not do too much damage, but in the later stages of the game with 5 ranks put into the spell and some AP to back it up the damage output of this spell is massive. Be careful using this spell early in the game as it drains your mana very quickly. This spell cannot be interrupted by CC, meaning that it will continue to run while stunned, knocked up, or even while in Zhonya's Hourglass stasis. The passive part of the spell is more relevant in the mid game for support Karthus, but still quite important. While toggled off, each unit killed by Karthus restores mana, increasing with the ranks put into the spell. Use Lay Waste to kill minions to restore mana (but don't steal CS from your ADC. Not until mid-game). Remember to toggle this off to get the mana restore effect.

R: Requiem
Put a point in this whenever you can, like most ultimates. Requiem is the iconic Karthus spell. Karthus channels for 3 seconds then deals damage to EVERYONE ON THE MAP. This global ult can be used to pick off escaping enemies, assist other lanes, deny objectives by putting the enemies at low HP and much more. Keep in mind that the cannel can easily be interrupted by any hard CC, putting it on full cooldown. And what a cooldown. This spell is one of the longest, if not the longest champion spell cooldown in the game. Make sure you are in a safe place to channel your ult before casting. Also, since the spell has a 3 second channel, you have to use it within the first 4 seconds of your passive or else you will be unable to cast it. It is often a good idea to cast your ultimate in your passive, as it cannot be interrupted by anything at that point.

(Example support Karthus game)


As Karthus support, you are a squishy, high-damage, poke mage. Be as annoying as possible to the enemy ADC and deny as much farm as possible by zoning with Lay Waste. Into the mid- and late-game you become a second mid-laner, and do Tons of Damage. Also: Have fun. It's a game. You might lose some times but make sure you have fun doing it.

Special thanks to /r/summonerschool on reddit for some help in making this guide.

Remember to try this in ranked first so you can impress your friends with how good you are at it later. (Please don't actually do that)