Karth is the simplest champ to play. All you really have to do is lane safe and get kills and assists off your ult. If you play him right you will be fed every single game and will become one of the most annoying/ksing/rageing champs in the history of LOL.

For runes you really want to have some AP and mana regen at the start of the match because his Q skill is basically your auto-attack. At the start of the match you should be able to moderately spam your Q skill and be able to get plenty of last hits with it. That is the reasoning for the runes. Remember Runes are for beginning game ownage, Items are for mid and late game. Don't try and change the build by buying those runes that give you like 30 extra AP at lvl 18 that is useless.

Alright Masteries is pretty plain and simple. You want to have that extra 15% spell pen in offence and the rest goes to Utility. Put 4 in "good hands" because karth's passive makes him have less of a down time after death and this will help out even more for those suicide karth moves. Also extra health and mana regen is always good in the start.

For items you need to get a meki pendent first with some health pots becuase with your runes and meki's you will be able to spam your Q skill moderately without looseing too much mana, too quickly. It is also important that you get Tear of the Godess as soon as you can because like I said you will be spamming your Q, which if you have tear's will cause your max mana to grow and make your AP go up when you make and Arch Angles staff. Your very next item is Zhonya's Hourglass. It is really important that you get Zhonya's before mid game for the team fights. Your next item is sun fire cape. Sun fire has a good AOE damage plus health and defense. sun fire combined with your Defile and a Zonyah hourglass is a deadly item/skill combo. The next items sequence does not really madder and is changeable. If you are owning with your ult I would suggest you buy more AP items like a death cap. If you are getting owned and need to survie more i would buy eather Gardens Angle or Rylai's crystal scepter. If you are doing a good amount of chaseing go with Rylai's it has a passive slow with will work good with your Defile and Wall of Pain.

For your skills I always max our Lay waste but always get defile second because every time you get a last hit at all with any of your skills you will get a small amount of mana back. your most used skill will be lay waste and defile. use lay waste as your harassing move constantly going back and forth spamming your Q. Defile is your team fight control move. what you should do is to wait for a team fight to start flash in press E and then activate Zhonya's hourglass. After that do not move unless and enemy team mate is running away with no health. If the team fight is still going stay there tell you die and play a suicide kart spamming your Q taking down all there health. Then after you die press your Ult. DO not press it when you are still alive in the middle of the team fight. Your Ult can be stopped with a stun or a nock-up. If it is stopped it will go to CD and you will have wasted it. Use Wall of Pain to save team mates or slow escaping enemies.

Karthus works best laneing mid. You want to get to lvl 6 as soon as possible because you need to get kills and assist with your ult. Doing this is hard late game but mid game and early game is very easy to get enough kills to get fed. The trick is to lane and keep the enemy away from your turrets while still paying attention to the rest of the game going on. If an enemy gets low Health go back behind your turret then ult. don't use it in the lane were your laneing enemy can get you. Just play it safe and make sure to time your ult right. Karthus is so easy to use and get fed just make sure that your not a noob and only use your ult to get you kills. Don't use it to ks only use it if your team has no way of getting that kill.