How to play as Kennen
Early Game:
You should harass as much as possible with Thundering Shuriken and Electrical Surge. It is useful to save the 5th attack on electrical surge to hit the enemy champions with if they are always surrounded by minions and you can't get them with a Thundering Shuriken. Don't be afraid to use Lightning Rush to get in a good position to Thundering Shuriken them, because energy is awesome. Once you hit level 6, you should be able to go in for a kill, given you are close to full health.

As you can see it the purchase part, in the build. I buy 2 "Rabadon's Deathcap", but sometimes
i buy a "Void Staff" instead of the second "Rabadon's Deathcap"

Get your 5th hit from Electrical Surge ready before going in for the kill. You should lightning rush in, and if for some reason you didn't hit them with it, flash onto their character so you aren't energy starved. Usually they will begin to run back towards their tower, allowing you to easily hit them with Thundering Shuriken. Pop Slicing Malestrom, Thundering Shuriken, Electrical Surge, and ignite on them. Usually this ends in a kill, and if it doesn't (because you missed or they are tanks), they certainly have to go back to base and heal.

Mid Game:
If you have a laning partner that can hold the lane by themselves or if a tower is down, don't be afraid to try to gank another lane. Use the same technique as you used earlier, as I find it the easiest way to make sure you land all your abilities.

Late Game:
This is the most important part of the game for kennen. You will make or break the game depending on how well you do in the team fights. Kennen's job in team fights is to burst down the enemy carries before they can deal too much damage. Most of the time, this will require you to enter teamfights behind the other team after the fight is initiated. Flash will be your best friend as you instantly get into the team fight with your ulti and begin killing the enemy carries. If you succeed, then all the enemy will have left will be tanks and melee dps. This should be fairly easy to finish off by the rest of your team. If the enemies are expecting you to do this, wait a little bit longer before entering the fight, after they have blown major cooldowns. Rinse and repeat, GG.

Skill Build Explanation

There are 2 or maybe 3 different ways to build kennen's skill order. The one I use most often is maxing out Thundering Shuriken first. If you are good with this skill shot, leveling it up will have the greatest effect on single targets and easily last hiting minions while laning. The downside is that if you are going for a kill and do not hit the enemy with Thundering Shuriken, you will have very little damage output on that target.

The second way is maxing out Electrical Surge. This will not only increase the on use damage but the passive as well. Maxing this will ensure that you deal a good amount of damage to any given target, since it cannot miss. I would recommend it for beginners while you are still learning the range and width of Thundering Shuriken. Also, maxing out Electrical Surge early will help with farming large groups of minions. At about level 12 or 13 you should be able to kill all the creeps of a wave with Lightning Rush and Electrical Surge. This will substantially increase your exp and gold earned during mid game, allowing you to get abyssal sceptor and zhonya's much quicker.

The third build would be to even out Thundering Shuriken and Electrical Surge. This creates a more constant damage output on enemies rather than a large burst every once in a while. It is pretty much average in the pros and cons of the skill builds above.

Tips and Tricks:
You can use Thundering Shuriken while in Lightning Rush form for a quicker throw to give the enemy less time to react.
Lightning Rush increases your armor and Magic Resist, so during Karthas' or Vlad's ultimate pop it to reduce damage.
If a stealthed unit has at least one mark on them, you can electrical surge to find out their location in order to hit them with another Thundering Shuriken.