hey i been playing karthus a while and i found this to be the most useful build to get kills with him. you will be weak early game but late game no one should be able to kill you. when in battle you should start by casting your E then into W, Q, and if someone try to run or for some reason you die cast your R if you die someone should have been low enough to ult if not multiple people. but through out the game and especially early game watch your map closely to see when enemy champs get low in health so you can ult and A kill them or B get an assist witch can speed you build up dramatically and around the time you get your rabadons and Arcangles you should be killing people real easily.
but some pros and cons about playing him is CONS/ he real squishy (easy to kill) no easy to get kills early game (before ult) also ( remember at lvl 6 and 11 you need the enemy below 250(6) and 500(11) Pro's/ late game high damage, after will of the ancients your damage with life steal will be ridiculous.