Welcome. This is my first cheat-sheet made on Mobafire. I give it my best first try.
So this is a build on how I play AP Teemo. Note that this is made for playing in Normal not Ranked match-ups. You could try it in Ranked but I suggest not to.

The first time I wanted to try Teemo out, my friends told me to play him as AP. I asked them "Not AD?". They replied "No, AP is way funnier". I tried and as the game kept going they told me what to buy and the skill sequence. My first game was fun to play. I got about 6/2/11. And so, I thought I could share it with you guys! :3

P.S.: My english is not very good, sorry "/

Enjoy!

Teemo is a legend among his yordle brothers and sisters in Bandle City. As far as yordles are concerned, there is something just slightly off about him. While Teemo enjoys the companionship of other yordles, he also insists on frequent solo missions in the ongoing defense of Bandle City. Despite his genuinely warm personality, something switches off inside Teemo's mind during combat so that the lives he must end while on patrol do not burden him. Even as a young recruit, the drill instructors and other trainees found it a little disconcerting that, while Teemo was normally charming and kind, he turned deadly serious and highly efficient the minute combat exercises began. Teemo's superiors quickly steered him toward the Scouts of the Mothership, which is one of Bandle City's most distinguished Special Forces unit alongside the Megling Commandos.

While most yordles do not handle solo scouting missions with a great deal of finesse, Teemo is remarkably efficient at them. His record of success in defending Bandle City from infiltrators easily makes him one of the most dangerous yordles alive, though you'd never know it by having a cup of honey mead with him at his favorite inn. Bandle City chose Teemo as their first champion for the League, and he has taken to it like a duck to water. His signature weapon - a blowgun - uses a rare ajunta poison he personally gathers from the jungles of ***ungu. To help cope with his lengthy periods of isolation, Teemo recently struck up a friendship with Tristana, a fellow League champion and fellow member of Bandle City's Special Forces. This connection is healthy for both yordles, though now Valoran's voracious media outlets circulate rumors that the friendship is turning into a romantic relationship. Regardless, Teemo is a crowd favorite in the League of Legends, and a pint-sized foe that many have come to fear.

''Teemo rides a thin line between chipper compatriot and unrepentant killer, but there's no one else I'd rather have as a friend.'' -Tristana

Just put the masteries as shown above. You want the AP bonus and the Magic pen and cooldown reduction. This is the best way I could find putting my masteries for AP Teemo. Not much to say, it's kind of standard for AP.

As for runes, you can go with flat AP marks but I like the Magic pen. For the seals, I'm using flat AP. Above there are to options for the glyphs. AP/level and AP flat. I prefer to use AP/level as it's more effective. You get your AP from Doran's Ring and Sheen early in the game. It makes it all balanced. Quins, put flat AP on those. It's not that hard, simple as that. :3

These are the Summoner Spells I prefer to play with Teemo.

Flash: Makes it easy to escape trouble. As you've got your W, Move Quick, you will not need Ghost.

Ghost: As i said, you don't need it as you've got your W, Mmove Quick. Sure, use it, but there are better options.

Ignite: Use it to finish off enemies if your abilities and basic-attacks doesn't.

Exhuast: If you don't want to use Ignite, then pick Exhuast. It's easier to 1vs1 an AD Carry with it and Blinding Dart. Sometimes, I go with Exhuast, if i get tired of Ignite.

Blinding Dart: Pick one point at level 1 and max it by level 9 as it is your greatest damage output.

Move Quick: I pick a point on level 3. You can chase down enemies and run away from them easier early in the game. Max it last as it is only good for running faster.

Toxic Shot: Pick it at level 2 for more damage. It works like ignite for a few seconds. It is nice when chasing enemies; they may sometimes escape but when low health, it will finish them off. Max it second for more damage.

Noxious Trap: Love these. These are your personal wards. Put them in bushes and other places. Many summoners are so scared, when they get low life, they try to run away by running in bushes. With Noxious Trap you can stop them from getting away as it slows your opponents. Deals a lot of damage with AP. At level 18 with almost 5/6 of your items, it will deal about 800-1000 magic damage. Mushrooms can also be good for killing huge waves of minions. Level it up by 6, 11 and 16.

Doran's Ring: Always start with it. +100 HP and +15 AP is nice and gives you Mana Regen which is good. If you need more ap and regen buy one more. One should be enough as you don't spam your Q.

Sorcerer's Shoes: Best shoes for AP's. Gives you Magic Pen which you will need.

Lich Bane: First core item. Gives you AP, Mres and Movement Speed. Sheen's effect is nice as you will basic attack after using Q, Blinding Dart.

Rabadon's Deathcap: GIVES ME AP! :D +140 AP and +40% is hell of a lot. Must have!

Rylia's Crystal Scepter: Nice AP and gives you health for more survability. Slows you opponent when using Blinding Dart or Noxious Trap.

Void Staff: Buy it after Deathcap as they will start stacking Mres, if they're smart. That magic pen will blow everyone in your path ;)

Zhonya's Hourglass: Can save you as your opponent will go for weak champs, you. Use it when needed, can save from ultis and ****. Gives armor as well, nice for going 1vs1 vs a carry.

You can if you will, pick other items:

Morello's Evil Tome: Go with it if you want Cooldown reduction.

Soulstelaer: If it goes well early-game, buy it, it gives you ap and cooldown reduction when reached 20 stacks.

Abysal Scepter: If the enemy AP is doing to well against you, buy this freaking item. Mres for defense and passive that is making them more injured. Sweet (y)

Thanks for reading my first cheat-sheet on Mobafire. I really appriciate if you comment on how you play AP Teemo, any questions or mistakes that I made. Every feedback is good for me.
I know this is short but I hope you liked it! Have fun playing, summoners! :3