Alright so this is my first guide for any League of Legends champion. Kennen is probably my most played and favorite, but I also play him slightly different than others. There are two huge factors that play into Kennen. The first and more basic is to get under your enemy's skin and poke them a lot. Getting good with his 'Q' skill shot is imperative to mastering him. The second is to master his stun!!!!!!
With the low energy cost of his Q, you can constantly be spamming it in lane. You should be using his Q whenever possible. Try to poke with it as much as you can, and when you can't, you should be trying to last hit minions with it. Early game farming is important with any champion, and is the same with Kennen. Building yourself up, getting as many last hits as possible with infinitely help you throughout playing this game...period. Late game, Kennen farms amazingly. With enough AP, you can run through an entire minion wave with his E, and then pop this W, killing the entire wave. This is a good strategy to damage an entire wave early game, and are trying to push.
Other than this, it is extremely important to MASTER his stun capabilities. Know every single way to stun. All of his abilities, when hitting an enemy, enable a charge. At three charges, you will stun your enemy. Kennen's 'W' is the most important skill in stunning your opponents before you have your ultimate. The passive of this skill is that every FOURTH star/shuriken you throw will have enable one charge. It is important to always have this ready when engaging with Kennen. With his 'W', you have a gaurenteed 2/3 of your stun if you auto attack them, and then quickly use his 'W's active. After this you can either skill shot with Q, or run through them with his E. I play against too many Kennen's who don't fully utilize his stun, which can prove to be very annoying. When you know his stun, it becomes easy to mess with your enemy.... which is fun, but can completely backfire if you're not careful haha.
I like to take Kennen's Q first, and max it first. Doing this will make your pokes do a decent amount of damage, causing your enemies to respect you. This is exactly what you want. I take my W second and max it second, and E is last.
First off, I have recently started to take Dorans blade first. Usually you will see a Kennen take boots, or a shield first. I found with either of these, I'm either too squishy(with boots) and/or I do not pose enough threat early game. Since your skills dont scale off of AP immediately, I found the extra HP and attack damage helps significantly. I personally think it perfects Kennen's early game.
After that you're going to need boots, maybe some HP potions to balance things out also. You are going to want to get your boots sooner than later since you've taken a Doran's Blade earlier, and Kennen relies on his quickness to get in and out of situations. After boots, depending on how well you are doing, you can jump straight to a soul stealer, or get the hextech for spell vamp. Without spell vamp, Kennen has virtually no health regen, this seriously benefits him and should be included in any build with him.
(I also include a soul stealer in every game I play with Kennen, simply due to comfort with how the item works. It is a gamble that I am willing to take, and more often than not, it makes any AP Champion very tough to deal with.)
After these, again based on how the game is going you should either get a Rabadon's Deathcap or Rylai's Crystal Scepter. If the game is going well, and you don't need the HP from the Crystal Scepter, jump straight to the Rabadon's. Rabadons combined with the extra AP stacks you can be getting with the soulstealer will make you very strong, depending on how quickly you can buy them.
For a long time I stopped including the Crystal Scepter from my Kennen build, but I have again realized it's importance. I personally do not think Kennen needs the slow, because if you master his stun, who needs a slow if somebody isn't moving? But the extra HP help significantly since Kennen is pretty easy to kill due to his low HP without this item.
After you have both the Rabadon's and Crystal Scepter, you're pretty much free to buy what you feel necessary. I like to grab a Void Staff in most situations, the 40% Magic Penetration it gives helps with anybody building Magic Resist. If you don't need that, you can get another Rabadons if you'd like, or whatever you want.
Regardless of the first item you get with Kennen, I still think he is always better with a partner. Yes, Kennen can hold down Mid fine, but I have found some insane combinations while playing with friends. Regardless of which you pick, you should always be utilizing your stun, and far reach of your Q. You should always be poking at your enemy, but do not over expose yourself as you are a squishy target. With a partner bottom, your stun will play an even bigger role for helping your teammate out. You can be either setting them up for a kill/double stun, or saving them if you are at the disadvantage. Kennen is very good with Morgana/Amumu/Cait/plenty of others. Keeping enemies disabled for as long as possible, combining with your teammate is insanely important. It simply makes everything easier when your opponent cant move.
In team fights with Kennen, I always make sure I am in the back to begin with. Kennen is not terrible at engaging, but when you do engage first, you will realize yourself dying a lot more than you should. If you get focused, Kennen is the type of character that gets vaporized in half a second. This doesn't help your team at all. During a typical team fight, I like to hang back for a bit and wait for everybody else to engage. Kennen is a NINJA, you should be isolating and frustrating your enemies, while also being in and out of battle quickly.
Once the fight has been engaged, springing in with his E and tagging everybody possible, targeting enemies logically. I then pop my W and Ult, which will stun everybody in the area. While they are stunned, you will also continue to place charges on them with your ULT finishing, and using your Q effectively. The main objective with Kennen is to not get yourself killed, which is a lot harder than it seems with some overgrown rat/ninja. If you do your job effectively, you'll notice yourself getting targeted which makes things just that much more difficult.
If it is possible, I like to save Kennen's E, because it is very useful to get out of fights. Sometimes you will find yourself using it to get into a battle, but with no way out. It is up to you to find the balance of when and when not to use it. Knowing when to use your skills will obviously make a huge impact on how you play.
I will be revising/adding more to this in the near future, but wanted to get this out there in the first place. Any criticism/thoughts are appreciated.