Basically as Karthus you just need to know how to aim your Q. Once you have his Q down you can harass and farm like a boss at mid. His W is quite useful it is a great slow in any situation and it reduces enemy magic resist allowing you to cause more damage with your Q. Requiem(R) may just be the best part about Karthus. Its great for helping teammates or ks'ing them but try to avoid that and its great for picking off enemies that manage to escape from fights or are just really lit.

The runes I use are mainly for a good laning experience. You will need the mana regen early because of how often you will use you're q to harass and farm. The items I use will not get you the most AP like stacking arch angels but with this item set you have the best chance of surviving plus dealing a load of damage