Karthus is a extremely fun to play champion who is amazing at farming.
He can rip teams apart when fighting his skills make him a hard target for melees that come within range of him and those that do are punished he is a strong person in mid pushing easily with his (E) defile

Most times as Karthus you will be mid unless there is another strong mid such as anivia

I used mana regen runes because karthus needs the mana regen to stay in lane longer I used magic penetration runes for enemies stacking magic resist
ability power runes because you want to harass them with lay waste early game

With masteries Karthus's passive gives you 20% time less dead with the masteries of reducing the time spent dead by 10% you get 30% less time spent dead so...
30% off 1 minute = 18 seconds so 42 seconds instead of 1 minute

Masteries are just the ones for ability power archmages savvy
4% health and mana regen and having longer buffs

Items...

start off with a sapphire crystal and 2 health pots
when you have enough upgrade it into a tear of the goddess
stock up on health pots if you need to

Next start buying rod of ages ideal time is to have it before 20 minutes
after getting your rod of ages you can stack them if you want or you can start building rabaddons deathcap or ryails sceptre so when you put up wall of pain (***) that will slow them enough for you to catch up use ghost if there just out or reach of the wall

once they run into the wall with ryails sceptre turn on defile and this will slow them as long as it keeps on them so now you have a Aoe damaging slow so it will be hard for them to run away

you want for your items ap but with some ap and health which is why you might want ryails and Roa so you have around 3k hp at lvl 18 with those 2 once you have RoA and ryails you build up your ap to around 600 so at lvl 18 your ultimate does 950-1100 damage

your lay wast should be doing 600 damage when your hitting the one target otherwise 300-350 damage and defile should be doing 200-300 damage

you will want to get lay waste first as a harassing tool next defile for farming which can kill whole minion waves easily with 0 ap lvl 5 defile dealing 110 damage a second in a team fight that will do a lot of damage when ur dead and in ur passive spamming lay waste with the free cost with the build 600 ap dealing 300 guaranteed damage when it hit 600 damage at least if it hits a single target with a 1 second cooldown getting a couple of hits off 300

300 x 3 = 900 if they stay near you for 4.5 seconds
plus if they are in defile circle 285 damage a second
enemys staying near you are getting dealth 1200 damage in 5 seconds
in a small AoE

With defile on while spamming lay waste you can anhilate squishys in a couple of seconds. When i am fighting a ashe or most dps.
A xin charged into me he did some damage but with my lay waste and defile I anhiliated him defile (285 damage) + me using lay waste (600 damage) about 900 damage and I destroyed him in 3 seconds

Karthus has amazing damage

The reason you take ghost and clarity is becasue karthus is really slow
and I find that flash doesnt do it because you can be caught even after flashing out of a 3 person gank then putting up *** (wall of pain) which they can just run around and put slows and stuns on you. So I find ghost better because you can use it for escape for keeping up with them with defile on and laying waste to deal continual damage

I use clarity because many times I run out of mana and I dont have enough manaa to cast requirm or to stock up my mana to harass some more with defile and lay waste and is often life saving or letting me get enough mana to put up Wall of pain slowing them and allowing me to finish them off

For jungling you want only the blue buff but many times I have gotten it from enemys in my passive killing them with requirm or my other moves so when I come back I often have blue buff and the red buff

Blue buff because of the mana regen with 3k mana and 1.5% mana regen and also the cooldown reduction helps alot with requirm with 90 second cooldown from the blue buff cdr with 110 second with no cooldown. Cooldown reduction items arent needed and blue buff is all you need for cdr.

Karthus deals a lot of AoE damage in team fights putting down Wall of pain to slow opponents escaping then catching up and slowing them with the AoE slow coming from defile because of ryails if its one of those annoying people who can get away because of their ultimates Master Yi with his immune to slows at lvl 18 finishing him when he has below 1000 hp which is for yi 1/3 - 1/2 his hp

Karthus goal is to deal out as much damage while playing safe
Combo should be defile lay waste they start running wall of pain defile and keep spamming lay waste

With ryails its much the same just that its much easier to chase with a right out slow with defile making it hard for them to escape and a massive slow from wall of pain you can keep damaging them with defile without slowing down to attack and lse ground

Karthus is a very good farmer with 110 damage a second with no ap and with 600 ap dealing 285 damage a second with defile you can take out creep waves in seconds. Making karthus a great farmer with a 1 second cd on defile I farm extremely well with karthus. Most times I find myself with to much gold because he's that good of a farmer

Karthus is good at killing very good at farming and is a good combination of pushing fast and killing 1 on 1 and in teamfights

Use his ultimate well tell your teamates how much damage your ultimate does and round it down a little e.g ultimate does 550 damage + 445 = 995 damage tell your teamates it does 950 damage just to be on the safe side if their low but not close enough get them to harass them until there within killing with your ultimate

get your teamates to if possible tell you who it is or ping them so you can check theres nothing more annoying than when they say ulti and there 50-100hp off

Using Karthus well will yeild a amazing amount of kills with alot of times I might die but i get double and triple kills
Make sure to use his skills right and accurately to really harass the enemy
Try to kite with Wall of pain slowing them then getting 2-3 lay waste's off
using defile can also be used to harass but doesnt have as great range

This is my first guide appreciate and comments feedback and positive criticism

Sorry about the writing im new to mobafire and tried changing it with the headings anyone know how to change font pls let me know =)