I've been playing Kennen for a while. I stopped briefly because there was a time when AS Kennen was better than AP Kennen, and when they buffed AP, I went right back in.
Lets start with Masteries:
I take 9/21/0, making sure to get the exhaust improvement and the spell pen masteries. I invest heavily on defensive masteries, because Kennen needs some time to really dish out damage, because of the energy dependence. The longer you are alive, the more damage you do.
What about Summoner Spells?
I like exhaust and ghost. Ghost is pretty much mandatory as Kennen, while exhaust will save yo ass from Melee champs, while helping you get kills early on.
As for Runes,
I go for health quintessences, and mixture of magic pen, CD reduction, and energy per second. Just use what you have lying around.
I learn my skills
Starting off with 1 point in Shuriken. Then a point in Surge, followed by 1 point in Rush. After this point, your priorities are Maelstrom -> Surge -> Shriken -> Rush.
You max Surge first for a very good reason. If you can somehow get a mark on your opponent, he cannot approach you until it goes away. Surge has a very large range, and with this, you can deny xp, gold, and even get kills. It is very, very important you max this ASAP.
When it comes to Items,
Start off with the Shield and a health potion. It will keep you alive for a very long time, and there really is no better item.
Second item you should get is Mercury Treads. It will get you out of many, many situations, You can opt for sorcerers, or even ninja if their team is stacked with physical damage. I don't like swiftness or mobility. You have Lightening Rush and Ghost. That should be enough.
Third item you should get is Rylai. Why? Because it KEEPS YOU ALIVE. Again, survivability is very important for Kennen. The order of subitems you choose to get is your choice. If you want more power to your attacks, get the scepter and tome, if you are feeling squishy, get the belt.
Fourth item is Zhonyas Ring. This is very important to get. More on why later.
After this, you should try to get some more ap, spell vamp, etc. I usually go abyssal then Will of the Ancients. That brings you to about 500 ap, with tons of survivability and spell vamp.
How should you play?
After hitting level 2 and getting your first point in surge, always try to get a mark on your opponent, and use surge whenever he comes close to you. Thats it. It is so easy yet so useful. That little mark will keep your opponent far away from you.
Before getting Zhonyas, be conservative, don't rush in unless you are sure you can live (and you have a lot of health so you could for the most part) and ult when there is more than 2 champs in range in teamfights. When you get the ring though, it all changes.
With the ring, you should probably be the second one rushing in the battle, after your tank. Rush in, mark everyone, use ult, and use the ring. For 2 seconds, you become untargetable while your enemies take terrible, terrible damage from your ult AND getting additional marks. After your ring runs out, Surge once, and not only have you done crazy amounts of damage, you have stunned their entire team, and you have a lot of energy from all the stuns, and you can shuriken for the kill or run away with another rush. Sounds easy, and it really is easy. A well played kennen will have soooooo many assists. You might not get the kills, but know that you are responsible for dropping their entire team down do half health and stunning them. Note that all the health, magic resist/armor, and defensive masteries you got was so that you can rush in and take as little damage as you can before you pop your ring. Remember that you also get armor and magic resis with Rush, so you will be pretty tanky going in.
And that's it. This was a quickly written guide, so I know it could be more polished, and maybe I will fix it later. But anyhow, this is the way I play Kennen, and let me know what you think!