Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
In a nutshell...
In this build, which has served me well, the objective is to build up Kenen's AP solely with the intent of killing enemy Champions. It doesn't even matter if you die so much, but it helps do damage and push the enemy team into submission.
The balanced skill sequence is such because most underestimate Kenen's long term effects on a mass melee. In one such instance, I rushed their team FIRST into combat and was able to get off the Ultimate, Lightning Rush, and then an Electrical Surge to stun 3 of the enemy champions, while also doing considerable damage to them, if not killing any of the weaker ones. A Thundering Shuriken and Ignite helped seal the deal on at least one other. By the time they had recovered and were preparing a counter attack, my team (always important) stepped in an prevented my death. A that point, when you have them on the run, you want Lightning Rush and Ghost to run them down and stun them AGAIN.
For Items, the usual and HIGHLY RECOMMENDED Doran's Shield and Health Potion to start, followed by Sorcerer's Shoes and then leaping STRAIGHT to a blasting wand. This is because at the lower levels your AP is not necessary to get kills on MOST champions. Once you have the blasting wand you have to make the decision to either concentrate on the Deathcap or get a Hextech Revolver first, but I recommend you head straight for the Deathcap. This is because once you have it, even with a Null Magic Mantle or Negatron Cloak, you will still be doing considerable damage. Then work up to a Rylai's Scepter, and after that work up to a Abyssal Scepter. And, if the game goes a long time, either work on some defensive items (I recommend Armors especially a Warden's Mail or Thornmail for champions like Warwick). Remember that in many games it's not how many deaths you avoid as much as how many kills you get before you die, so pick up another Deathcap if you got the kills/money.
Spells makes your mastery
Mastery: If you are going to take Ghost, take Haste; it's one point that improves it. If you are going to take Ignite, take Burning Embers; seriously. The listed mix of mastery will allow Kenen to balance some of his weaker areas while also improving his main strength: Ability Power.
Runes: All AP or mix it up to keep Kenen alive longer: well... probably go with Balance, he is, after all - the one who promotes: "Balance in all things." -Kenen
A lot of Kenen players know this, but for the rest of you:
Once you get your AP above 400, you can solo push lanes with the slightest of ease, just E, run straight through the whole line of minions, then double back so they are all in range, then W, and that's all she wrote for that group. And they are spaced out to allow your energy and abilities to come back. Use your Q for those BIG minions.