After a team fight has initiated, use Lightning Rush to apply marks to as many enemies as possible, followed by Electrical Surge and Slicing Maelstrom. This combo adds two marks initially, followed by one mark for the stun, and then adds an additional two marks, leaving any runners ready to be stunned with Thundering Shuriken . Alternatively, saving energy and waiting for a second Electrical Surge will result in a second AoE stun.
For this combo, wait the longest time possible between the Electrical Surge (passive) (which completes the 1st stun) and your Slicing Maelstrom (which completes the second stun) to regenerate Energy, land free auto attacks, and position yourself behind the enemy.
The key to playing well is learning how to chain his combos together to be able to land free damage on the enemy while keeping them in a disadvantageous position.
A good way to build Kennen is a balanced build, which focus on building tankiness as well as damage. With all three skills at rank 2, Kennen becomes a powerful enemy.
Slicing MaelstromKennen is amazing for turning team fights around. It is key that his R is used as much as possible against multiple opponents, but only at the right time.
Remember that Lightning Rush also provides you with a great boost of your armor and magic resistance meaning it can save you from fatal situations like Karthus' Requiem or skills that do damage over time, notice however that it won't reduce true damage.
One of Kennen's biggest strengths is his flexibility of item builds in any given situation. Kennen can easily be built either as an attack damage carry or an ability power based carry. He's also a very powerful top laner in both attack damage and ability power based builds due to his decent attack damage scaling and Electrical Surge passive and split pushing ability because his Lightning Rush can serve as a good escape mechanism in sticky situations as well as serving a good pushing skill in conjunction to his Electrical Surge active.
Ability Power build strongly utilizes his Thundering Shuriken, Electrical Surge's active, and Slicing Maelstrom. The ability power build brings more teamfight presence and large crowd control stuns on the enemy teams who tend to be grouped together. Because Kennen needs to be in the frontlines to utilize his ultimate, he needs to build a bit tanky in addition to ability power since he will most likely be focused on. The ability power build synergizes well with champions who have heavy area of effect damage (i.e. Ezreal, Ziggs, Amumu, and Nunu) or dive heavy team compositions.
Attack damage builds are almost similar to an attack damage carry where he puts more emphasis on autoattacking because of his Electrical Surge passive scales in attack damage and his strong self-crowd control and utility ability with his Mark of the Storm, something that most attack damage carries lack with a few exceptions like Ashe and Varus. Because Kennen uses Energy rather than mana, he has better sustain than many other attack damage carries except Sivir. Building Kennen as an attack damage carry is recommended for those who have difficulty landing his Thundering Shuriken, laning with supports who lack any forms of healing or sustaining the attack damage carry like Lulu, Blitzcrank, Leona, and Thresh, or team compositions who tend to focus on a single target. Keep in note that attack damage carry Kennen tends to fall flat late game against other late game oriented attack damage carries like (Tristana and Kog'Maw) because he is really reliant on autoattacking where his range is equivalent to Vayne and lacks good attack speed/damage steroid unless he is fed early.
Getting double Doran's Blade early game allows Kennen to be a strong lane bully with the passive of Electrical Surge as well as give a little survivability.
Sheen and Lich Bane are effective items on Kennen. If Kennen is played as a caster, Lich Bane is useful for increasing the amount of damage he does, especially since his Thundering Shuriken can be used every 4 seconds at rank 5.
Since Kennen usually relies on being in the middle of their team an Abyssal Scepter can provide you with more damage and survivability while the negative aura will also boost the damage of your allied magic damage dealers.
Since Kennen does sustained damage using energy, building an early Hextech Revolver is a good idea for him, particularly if you are facing a champion who has their own built-in sustain like Renekton, Vladimir, and Yorick.