One of Kennen's greatest powers come in his ability to quickly get rid of waves of minions. One Lightning Rush >>> Electrical Storm is usually enough, once you get a level 5 Electrical Storm, to wipe out a wave of minions in the 2 seconds it takes to run in to the minions and hit your skill.

AP is big for Kennen, all of his skills scale with it and since you can cycle through all 4 of your skills relatively quickly you can take people from full HP to almost dead if not dead in a very short amount of time with enough AP. I use the runes that level along with you because with all of them, by the time you get to level 18 you are looking at a boost to your AP to the equivalence of a medium grade item.

Exhaust: I believe this is the most important Summoner Spell for Kennen. You are squishy so when they get in range to fight you, you need something to take care of that. Exhaust is a great tool to laugh at them, and give you a little more time to either get away, or deal the extra damage you need to finish them off.

Ignite: The only spell you can get that will deal damage to the other champions, which make this a great spell for you. You should be making them fear your power, which means they will try to run from you. Getting them almost dead and running off with ignite left on them to finish them off from the safety of not next to the action.

Flash\Ghost: This is another viable option for Kennen. Since I condone soloing lanes at the end to push your minions to their base, having another escape mechanism is always a good choice.

Rylai's Crystal Scepter: The most important item you will buy for Kennen. Slowing your opponents so they they will stay trapped within your Ultimate will increase your damage output quite a bit. It will also help your teammates keep the pursuit on them

Sorcerer's Shoes: This item will help you break through their resistances. Pretty much all there is to say about that. I would choose this over Ionian Boots because Kennen doesn't have the energy to really support too much of a constant flow of skills.

Will of the Ancients: A combination of AP and Spell Vamp is a nice addition to your arsenal. It also gives the rest of your allies a bonus as well. This item will help with your solo laning and group fight survivability.

Zhonya's Hourglass: The second most important item you will get. Lightning Rush >> Slicing Maelstrom >> Hourglass is a practically free, safe, sexy damage. The best part about it is that you become untargetable, so it gives your team some time, where they are trying to target you and realizing they can't, to take them out while you apply constant damage to the fight.

Rabondon's Deathcap: Gives you the most AP, in a single item, in the game.

Everyone builds a 21 defense build with Kennen, I am not saying they are wrong... but I am saying that with the play style of Glass Cannon, I feel that 21 offense 9 Utility suits that play style much better. Utility gives you some Health Regen, and an Experience and Gold Boost, where Offense give your a nice buff to your offensiveness. You are a squishy champion... even with the power of Defense Masteries, you are still a squishy character. "The best defense is a good offense".

Crit Masteries: To be honest they are mostly a place holder spot to get to Havoc, but having 12% crit in the beginning of the game does help here and there for dispatching minions and early level champion harass.

Attack Speed Masteries: Mostly the same as the crit masteries, but it also makes it easier to get in the last hit on minions early on, while yes I know not a huge help, it is something none the less, and like I said, mostly to get up there to Havoc.

Burning Embers: Early game, this provides a nice boost to AP while your Ignite is on cooldown, late game, not so much, but getting the early game advantage is important.