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The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This is my take on Kennen as an Ability Power / Attack Speed Ninja.
This is by no means the only way to play Kennen, but after experimenting with AP, AD, AD/AS, and AP/AS builds, I have decided that AP/AS suits my playstyle best.
A few words about this build and my playstyle with Kennen:
Kennen is a lightning ninja, so he should attack quickly and hit hard with his abilities. Recently, Kennen recieved AP ratio buffs to his skills, and I feel that he is now best utilized by maximizing his damage output via q,w,r and his stun capability.
Pros of AP/AS Kennen:
High burst damage potential.
More marks, more stuns.
Strong all game long.
Slightly less durable early game (no hp quints).
Increases stun capability at the cost of some burst damage.
I choose 9/21/0 to offset the lack of magic pen runes and flat hp quints in the rune build. Defensive masteries also give extra attack speed and ability power. Other viable options: 21/0/9, 21/9/0
Alacrity marks/quints provide the best bang for your buck in terms of laning phase harassment. Hp/lvl seals for survivability when you need it ( hp/lvl > flat hp at lvl 5).
AP/lvl glyphs to offset the 55 AP of Nashors tooth in the item build.
Many good choices here, but I prefer to have some escapability. Since Lightning Rush is like a mini-ghost, I take Flash. Then Ignite provides some extra finishing power and healing reduction. The only crucial thing is the escapability, since Kennen tends to get into the middle of the fight with his ultimate.
The goal of this build is to get your AS up as much as possible without sacrificing much AP. 55% from Nashors, 26% from runes, and 4% from masteries brings you to 85% AS. This will almost double the rate you passively apply marks in team battles and make it more likely you will get an extra stun during a 1v1.
I dont really like "fixed item builds" for characters, and prefer to gear according to my opponents strengths/weaknesses, but I do advocate a core build: Boots, Nashor's tooth, Zhonya's Ring, and Rylai's Scepter.
Possible starting items, in order of how often I start with them:
Amplifying Tome + 1 hp pot
Doran's Ring + 1 hp pot
Boots + 3 hp pots
Dagger + 1 hp pot
I base my decision by how much I anticipate getting harassed and the relative squishyness/tankiness of my anticipated laning enemy(or enemies). The tome for ranged enemies, the ring for big harassers, the boots for faster champs, and the dagger for melee champs I expect to be able to auto attack more frequently. If I do pick up Doran's Ring, I usually sell it to finish either Zonya's or Rylai's. By then you wont need the hp or the ap.
About 2nd level boots:
Choose your boots wisely. I strictly itemize these according to the enemy team makeup. For enemy champs with snaring ults, or teams with 3 or more primarily magic damage champs I choose Merc Treads. Otherwise I may pick up Ninja Tabi to synergize with the defensive masteries I go with, or perhaps swiftness boots. Most of the time its Merc treads, which is why I included them in the item build section. Very rarely do I buy anything else.
Possible items to get after Rylai's:
Offensive: Abyssal Scepter, Lich Bane, Guinsoo's Rageblade, Hextech Gunblade
Defensive: Guardian Angel, Banshee's Veil, Quicksilver Sash
As you probably know, playing Kennen is all about stuns, and comboing his abilities to get stuns off at the right moments.
Harass as much as possible, but dont forget about last hitting. Your attack speed makes it easier to get those precious last hits, and also lets you harass with W more often. Harass the hell out of them. Eventually they will learn that anytime your passive procs, they better back up. Use it to push them off of last hits and deny them. Attack speed gets the job done. You can get two marks from your W and then a third from Q for the stun. Lather, rinse, repeat.
Mid game / Late game:
Nothing special here. Just dont forget your Zhonya's. I use it frequently after the following combo: E -> R -> W -> Zhonya's.
And thats what AP/AS Kennen is about. Nothing fancy, just the right amount of attack speed to make him excel. More attack speed is really not necessary, and will probably make your damage output suffer. So dont go that route. Stick with this core build and build into more damage, or some survivability, and you should do well .: