Not Updated For Current Season
Kennen can be very versatile if played correctly, and you may even carry your team. All with the help of Zhonya's Troll. Zhonya's Troll (Hourglass) is your main item and will help you to stack Mejai's Soulstealer which leads to an amazingly OP ninja.
WHY DO YOU GET ZHONYA'S First?
Your first big purchase will be a Zhonya's Hourglass. This is because typically team fights will begin earlier than expected and if you want to be a useful Kennen you will need to be able to put out some damage. Now of course the enemy team WILL focus you when you ult them, so having Zhonya's Hourglass early helps to get plenty of assists and kills. This helps to stack your Mejai's as well which in turn lowers your ult's cool down while at the same time still applying extra AP from Rabadon's Deathcap. Even if the enemy team is not team fighting yet you will still want to get Zhonya's for the armor defense that will help you in a 1v1 vs. a tough melee. Once team fighting does begin (if it hasn't) you will then be completely prepared and not have to worry about trying to farm quickly for zhonya's. GOOD LUCK & HAVE FUN
The Mastery set is pretty basic. 9 points in Attack for the Magic Penetration, and 21 points in utility taking 1 point in "Blink of an Eye" and "Presence of the Master" for reduced flash cooldown. Also remember to get the extra ability cooldowns with "Intelligence". I also take 1 point in Cripple to improve your exhaust spell which will allow your team to better take down an enemy (remember carries can still play as a team).
Magic Penetration marks will help you in the early game to get last hits and possibly kill an enemy champion that will just barely escape. The reason why you don't get too much Magic Penetration is because most summoners commonly do not build magic resist and the base magic resist is quite low for many champions and does not go up very high.
Health Seals will help you to have a bit of survivability in early game which will be very useful as Kennen is an easy early target to take First Blood on.
Cooldown Glyphs will help you to get your ultimate back quicker which should net you much more assists and kills. Also farming is increased when your E and W come back quicker. The reason why it is cooldown per level is because early in the game you don't really need much cooldown because your ultimate is not very high level and doesn't do much damage yet. Also you should get blue buff whenever possible to help cooldown your ultimate even more which will result in major spam troll of Kennen's perma-stun abilities.
AP Quintessences also are useful late game as they generate a lot of AP per level so you will have a slightly even more dominant lead in late game.
Exhaust & Flash~
Exhaust is mainly used to take down enemies if they still are escaping after you have spammed all your spells at them.
FLASH is a MUST! With Flash you can flash into an enemy mob and initiate with your ultimate, then after activating Zhonya's Hourglass you can completely be safe while doing damage and adding CC stun to your team composition. After your Zhonya's effect ends you should usually back up a bit or continue to spam your skills if you feel that you can take down an enemy champion(s).
Alternates: You can substitute Exhaust for Cleanse if you find yourself to get caught in tough situations a lot. If not you can usually just use your E ability to quickly escape an enemy gank. But Cleanse can still be a useful asset to your champions escapability.
Farming should usually just consist of using shurikens to quickly deal the last hit in early game. Once you have a substantial amount of AP you can go E into mobs of minions and then W them all at once. This should generate a good 50-200 gold each time you do this to a mob of minions.
Typically Kennen gets Q W E because people like to harass early in the game with their mark of the storm passiv combo from W. But i prefer Q E W because you never know when you will find yourself getting ganked or being harassed right at level 2. If you are getting killed yout E is a great way to escape and also can be useful in traveling around the map quickly. You must remember that Kennen is an energy-based champion meaning if you are at your fountain running back to defend, you should press E to get some movespeed and your energy will regenerate by the time you arrive at your destination. Also, as suspected always remember to level up your ultimate ability whenever possible (levels 6, 11, and 16).
When Playing as kennen you always want to look for open opportunities to gank your enemies, ganking early with kennen is usually much easier due to champions and tanks more specifically not having very much defense and hp. If you are mid make sure you can take time away from your lane to go gank, and if you are in a duo lane make sure your partner will be okay without you. Always ask if anybody needs a gank or ask before you go to gank. Communication is very important.
Also if you are level 3 it is very helpful to your teammates if you stun the enemy champion before running away if you are getting ganked. Typically you will be able to land a shuriken and W then E to move away quickly. Remember Team Work is crucial for Kennen to be an appreciative carry.