Not Updated For Current Season
This is a solid AP build for kennen.
Start of with buying an Amplifying Tome for the extra AP which will help you get the early game kills. Save up for Mejai's Soulstealer as soon as possible so you can start stacking up, then Boots of Swiftness. Next go for Rylai's Crystal Scepter, as Kennen is pretty squishy and you will need the extra health for upcoming teamfights. After that go for Zhonya's Ring so you have a decent ammount of AP. Near the end of the game buy items like Abyssal Scepter and Void Staff for the magic resistance and penetration.
Early game try to harass enemies in your lane as much as possible using your Shuriken to inflict marks. Use your lightning rush to run through large groups of enemy minions. It will inflict marks so you can finish them with your Electrical Surge. This is a great way to farm for gold. During mid- and end-game save your ultimate for big teamfights. Mealstorm will deal a significant amount of damage to multiple enemies and apply marks, which will allow you to hit them again with Surge. Catch up to fleeing enemies using Lightning Rush. Don't get too cocky by rushing in first with your ulti, as your stacks are quite important. Let your tanks go in first, they are there for that.
Masteries and runes are self-explanatory. I prefer putting it all into AP, as it does make a difference once the game starts to advance. Even though you could put them in critical strike, or mix it up.