This is my first build on Mobafire, but I have been working with Karthus for quite a while now and think I've found a good build that really suits him. It is centred around getting early magic penetration, then buffing AP as much as you can to really hit home. This makes his Q ability, lay waste, knock down health bars easily. The extra penetration also helps Requiem a huge amount, and after you get your AP up you can easily get triple kills and more.

General tips:
Last hit minions. The steady stream of mana gotten from lay waste will help tremendously.

Get the blue buff whenever possible. 25% cooldown reduction and extra mana regen can really put you over the enemy in a fight.

Don't overextend. Chasing an enemy down is just asking for your squishy self to get owned by a jungler or opportunist, like Udyr or Tristana.

Ration your mana. Using defile's active can drain you very quickly; only use this ability as a last resort or for quick farming. If you use defile well late game however it can be mana neutral; just activate near a large minion buildup.

Finally, have good communication and don't waste your ultimate. Requiem can be a game changer, and using it to pick of one person or not knowing when to use it can really be a waste with the crazy long cooldown.

In short, harass and lay waste to your enemies. In long...

Lay Waste:
Your lay waste ability is an excellent farming ability in the beginning, especially when coupled with defile. Use lay waste to last hit minions; getting extra mana and gold can really help you. Harassing the enemies however is the most important part of lay waste, and is the reason why you buy the boots so early. Lay waste does double damage when it hits a solo enemy, so put it's range to good use by shooting it behind an enemy, leaving them as the sole target. This really keeps them off the front line, keeps them from harassing you, and will allow you to pick up a kill or two early on if you are against a slow champion like Twisted Fate or Kog'Maw. Don't get overzealous however and chase down low enemies, Karthus is VERY squishy and will die if any enemy shows up to assist.

Defile: The use of the passive was noted above, so this part is only for the active. This skill is the most mana draining skill in Karthus' set, and I find it to be largely unnecessary until later game. Early game your health is too low, and mana reserves too small to get close and rack up damage. It is VERY important you DO NOT use this skill on anyone until late game. Using it drains very valuable mana, and may leave you with not enough to use lay waste and finish of an enemy. However, late game this skill may have some use. I use this skill when guarding an ally's retreat; if an enemy chases us (and my wall of pain is in cooldown) I'll activate defile and it usually makes enemies think twice about staying around me. The other use is on minion buildups, and the way you would use it there is pretty obvious.

Wall of Pain: This skill, as you may have noticed, I leave underleveled until I'm a high level. However, it is very useful in team fights and saving yourself from ganks. Simply throw this wall up if someone tries to side-gank, behind you if you're being chased, or behind enemies if your team is getting them low and you need to prevent an escape. Very simple, very useful.

Requiem: This is the reason most people play Karthus, and actually requires little explanation. However, I will say that it is best used early on when enemies have 2 or less bars of health, and later on you'll just have to size up your enemies. After playing a lot of Karthus, one look at the bar and you'll know who you can kill. Be sure to have good communication with your team, or the power will be wasted and Karthus must suffer the wrath of the super long cooldown.

Strength: This build has a lot of magic penetration and AP, making lay waste pack a punch and making requiem more than a 50 health mop-up skill.

Weakness: The only weakness to this build is Karthus' low health, which it would be hard to correct while still staying on track for the AP and magic penetration. So, keep an eye on your health at all times and don't be afraid to go B. This build used to have a MAJOR mana problem, as I would rush void staff right after my sorcerer's shoes. So, I moved an archangel into the build as it adds manna after every ability you use, which is a perfect fit for Karthus' lay waste usage.

The masteries and runes I have used in this build are a little unorthodox, but on the other hand if you always make what is expected no better builds get made. So here goes.

My masteries on offense make sense, but some may ask why I have so much in defence and utility. These are, obviously, to make Karthus have more health, armor, and magic regeneration which are all weaknesses of my build. My marks and seals are all about making up for Karthus' mana deficiency in my build, and the rest are to help keep Karthus on the field and less of a squishy champion.