Sometimes the most effective way to kill enemies is to run in after teamates, defile, and lay waste spam. Now because your passive is AWESOME keep spamming if your dead and cast your ulti if there low, Usually after you have spammed (if your teamates haven't killed them) you should be able to get 1-3 kills making your death worth it.

DON'T USE DEFILE UNTIL YOU HAVE YOUR FIRST ARCHANGLES. It is very important not to use defile until you have you first major item. It drains way to much mana and not enough health of minions. Not much else to farming except that when your defile is really effective you should out level most champs in the game pretty fast.

So first off, You should lane mid with karthus. He is by far the best mid in the game in my opinion. Using the Sapphire Crystal you will be able to spam lay waste and harass enemy champions very easily (Try not to use this on a champion when there is a minion nearby because it does less damage when it hits multiple targets). Once you get level 6 the champion should be decently low (If you have been harassing good) and you should be a bit more aggressive and get them to 1 and a half bars to 2 bars and ulti (depending on their magic resist) and land first kill. This is my first guide so please bare with me. Let me know how this build goes for you and if I should add anything.