Alright so this build focuses on Kennen's AP abilities, and I know a lot of people prefer AS Kennen but just like with AD Ezreal I can't stomach only making one of his abilities work for you. Kennen has a lot of potential as a mage, and if you can really get good with skillshots, you'll leave your enemies dumbfounded and frustrated.

The pros I've noticed playing this build are:
Good lane control in mid against a good number of carries.
Insane harassment when laning with someone.
Kennen becomes a very good initiator mid-late game.
Very hard to lose your target or to be caught.
By late game your Shurikens are not only worth something, but are feared by anyone who's not stacking MR like a tank.

There are some cons though, and those are:
Very vulnerable to ganks/damage in general early game.
Disables, especially silence, shut him down easily.
Banshee's veil is your bane.

Alright so a quick overview of masteries, putting 21 in defense while avoiding crit means a couple of things. First of all it means you have a steady stream of mediocre damage from your basic attacks, you're not here to play Tryndamere, so don't bother aiming for arteries. Second, you increase your harass-ibility early game dramatically, focusing on your shuriken might sound like putting all your eggs in one basket, but that basket has a much longer range than your base attack, costs virtually nothing (due to energy regen rates) and has a possibility for future stuns simply by hitting them, that's a worthy basket in my opinion. Third, it means you'll farm a little bit better and you'll get CDR all rolled up in one tight little package.

The 9 in defense couples with the runes I've chosen, 3% dodge + 2% dodge = 5% dodge and a speed boost, dodge, sadly, is your only real defense early game, which is great against physical damage heroes, because it means you can avoid a little damage here and there, while using your brush to your advantage for the rest of the time.

With the rune page I've set up you get 22 AP, 3% dodge, 8.5 MP and some CDR, basically you're focusing on one thing, dat shuriken, because at level 1, with 22AP from runes and more from masteries, you can easily cut a teemo's hp bar down in just a few shurikens.

Moving on to skill sequence, shuriken is the bomb, literally. Once you get to mid-late game, your shuriken is going to start doing upwards of 400-450 damage... every couple of seconds... get it upgraded asap and you'll be able to control lanes without a problem because no one will want to stick their head into that. You really only need the lightning rush for one thing, GTFO, that's about it, so only get one rank until you have to get more and you'll be fine.

Start with a doran's ring, I know I know, the mana regen is lost on Kennen, but the little bit of hp and the AP is exactly what the doctor ordered.

Early game is going to be your time to set things up, instill fear into your enemies hearts with ~100 damage shurikens. If you're in mid and you've got anything but a tank, then your job is simple as can be, keep moving, try to be unpredictable, and toss shurikens as your enemy presents themselves as a target. Feints are your best friend, duck in and out of things; step forward like you're going to do something and then pull back, see if you can bait them out and then punish them for it. The great thing about Kennen's shuriken is that its very hard to dodge if you can get them in the middle of its range.

Once you've got your Electrical surge, pound it every time you hit them with a shuriken, and try to auto attack minions a few times until your next auto attack will apply the passive ability, and couple that with your shuriken + surge combo for a stun and a few auto attack or two.

If you're laning you've got it even easier, try to lane with people who can stand in the lane and not worry about taking a hit or two (Rammus, Malphite, Mordekaiser, Shen, Olaf, Trundle, etc) let them do most of the minion killing and dive right into the bushes, use your shurikens to keep the enemies either away from the creep line, or wary of standing still to long. Do your damnedest to STAY IN THE BRUSH, Kennen's shuriken becomes a whole lot easier to dodge if the enemy knows where its coming from.

SIDENOTE: Don't push too hard, its easy to shove the enemy back to their tower and terrify them of coming out again. THIS CAN BE VERY BAD! A lot of times it means you won't get any early game kills. So unless you have a lanemate who can really pound on the enemy at their turret try to let them push out, let them think they're still in charge somewhat so they will get greedy and you can kill them.

In either case you've got to avoid death as much as possible, a few deaths can set you back quite a bit on rushing Zhonya's hourglass, unless you've got a sound strategy for first blood, save your Exhaust for defense, for when Twitch appears near you or Master yi attempts to cut off your escape route. Once you have 1200 jump back and grab Hextech revolver, this will be your saving grace for quite a while. Kennen's high magic damage output with his shurikens means that every hit is another 15-25 hp in your pocket.

Mid-game is going to be painful, I can say if you ever go negative in k/d ratios, this will be the time. Now is when a good number of heroes are starting to shine more, but here you are saving for hourglass little by little. Try to stick next to your friends, avoiding too much solo time because Kennen is too squishy and too slow to do much by way of defense. Your shurikens will ward off the squishies, but you won't be able to do anything to the tanks, so don't pick fights with anything that will keep you in combat for long, hit and run from the bushes. You'll need some boots of speed quickly, and then start grinding for that hourglass. It might seem like a stupid idea while you're racking up a few deaths, but its worth it in the end.

Late-game begins once you get hourglass, this is your cake walk. Getting the deathcap will probably boost your AP up enough that you're starting to really dig those flying dynamite sticks they call shurikens, but Zhonya's hourglass makes it all worth it. Adjust it so the item is in the second slot, wait until level 16 before attempting, and then get a teamfight going, let people know you've got Zhonya's, and group up. When the enemy team groups up to fight you, charge! Pop lightning rush and your ult, and hit a couple on your way in, but don't give them more than a second to react, and once you're firmly in the heart of the enemy's position, hit Zhonya's like you mean it. Congrats! you are now a lightning storm, causing large chunks of damage, stunning enemies, providing plenty of chaos for your teammates to take advantage of, and being untargetable for 2 seconds. This is an amazing contribution to the team, it'll get you dozens of assists and probably a few kills as well.

After Zhonya's and Will of the Ancients (Hextech revolver lvl 2) its all supplemental, Void staff and Abyssal scepter are my suggestions since as the game progresses you're going to run into champs that start stacking MR, and you need to get rid of that. Make sure your spells hurt.

On the other hand, sometimes Kennen needs some defense, FoN works very well because of the additional move speed, and things like thornmail and Warden's mail will help you make physical dps think twice before hitting you, which is hopefully all the time you'll need. Rylai's is alright, I know that sounds odd, but it doesn't much help because HP doesn't really give you a good enough boost to matter, 8 times out of 10, you die because you get disabled and held there, and you die in seconds. No additional amount of life is going to help that.

I've experimented with making it a hybrid build, adding a Phantom dancer and a Bloodthirster into the build, and it does have success, but if the game lasts for 45 minutes or more you'll start to wonder why you aren't nuking as hard as you used to.

Silences **** your day up, in every sense of the meaning. Kassadin can be real trouble, Leblanc is a royal pain. And even a few of the smaller silences, if placed well, can ruin your dive-bomb attack. If this starts happening, try to be the second to dive in, assure your tank you'll be there, and hit them from a different angle, hopefully they'll focus on him long enough to let you slip in.

Brush is your friend!! Try to make sure that no matter where you're headed, if you're going through the jungle have your electrical surge passive ready (shuriken glowing like a sparkler) and stick to the brush whenever possible. The thing is that every three stacks will stun, so if you catch a jungler, a healer, even a dps who is just passing by, you'll get to shuriken -> electrical surge -> auto attack, and while they're stunned and already missing 1/3 to 1/2 of their life, you get roughly 2 auto attacks before they wake up, and by then your shuriken is ready to go again, and you're only 2 hits away from another surge proc.

YOU ARE A NINJA, act like one, use surprise and your disable to turn the tables in your favor.