Make sure that when you are farming that you do not go pass the half way point of your lane that makes you easily gankable. karthus has a long range on his q so you dont have to worry that much on an enemy's skill shots. The mana regen runes helps you keep going remember not to spam your q. karthus is extremely good at farming with his q. Dont use your e to farm. you use your e to push the wave back and recall when the enemy isnt there. remember at early levels you use your q to farm at one minion at a time DO NOT LET YOUR Q HIT TWO MINONS IT REDUCES THE DMG BY SO MUCH
(Minon)o <---Q right there you dont have to place your q directly on the minon. If you are taking so mch dmg and need to back you have your teleport derp :D another nice choice for summoner spell is exhuast you dont need ignite on karthus :D WHEN AN ALLY DIES LOOK AROUND THE MAP TO SEE IF ANYONE IS LOW IF THEY ARE YOU PRESSS RRRRRRRRRRRRRR. try to use your ultimate after you die. your cast time for your ultimate is like 3 or 4 seconds between those time you cna pop 2-3 lay of wastes after like your 3-4th lay of waste you wont be able to active your ultimate if you are dead your passive lets to kinda stay alive for 7 seconds so 2-3 sec lay of waste and the rest of the time you have left you use your ultimate. during laning You just have to be passive for a bit. with mr runes you can kinda trade with your enemys pretty well if you want to. in team fights you dont go all in till they all blow their cc on your team mates :D

pros: ks mastaaa tons of dmg even when dead team fight changer! little mana required for early laning
cons: needs farm pretty squishy if you dont have roa long cool down on your ultimate -.-