Well what could I say about Teemo? He's running really fast on that short legs and his poison is annoying to your enemies. In this build i went AP/AS, because it's really effective on teemo. AP gives more power to toxic shot, which hits with each aa and AS makes you apply this bonus faster. So enjoy and please - try it then vote/comment.
I can make some mistakes, my english isn't perfect, so please don't downvote because of a wrong word or smth.

Pros:
-Fast
-Mobile
-Free Wards
-It's hard to gank on him
-Great damage mid-late game
-Not very mana-dependent
Cons:
-Squishy
-Not so easy to play
-Mushrooms are hard to place in teamfight, so practically no AoE damage

Now about skills. I've chosen Toxic Shot as my first skill. You can also take Blinding Dart, but I prefer poison. Taking Move Quick on level 4 lets you buy malady before Berserker's, so you'll have some AP/AS boost first.
Remember about placing your mushrooms, wherever you can! If you're mid place them in brush and in these 4 pathes to mid. It would make you ungankable, with activating your Move Quick.

Taking boots as first item makes you more mobile. With Move Quick you got about 390 speed on 4 lvl, with just Boots of Speed. Malady gives you some AP and AS boost and a nice passive, which helps your poison. Then finish your Berserker's Greaves. That gives you more speed and some AS. Then Nashor's Tooth. AP and AS - great item for Teemo. Also some mana regen, so you won't have any mana problems from now. CDR let's you place more mushrooms in less time. Then Phantom Dancer, another good item for you. It gives you AS, movement speed and Critical chance. Then build Guinsoo (I'm sry, I made a mistake and in build there was a Rylai instead of Guinsoo, now I fixed that) which gives you AP, and AD. With full stacks of it you'll have 2.5 AS, so you don't need more AS items. At last item I've chosen Hextech Gunblade. AP and AD are always nice. Life Steal and Spell Vamp will give you some survi. If you need you can sell boots after buying Phantom Dancer and make some better survi item. PD and Move Quick will give you enough speed.

Flash - always helpful, to catch a free kill, to run away behind a wall. Very good spell with lots of uses.
Exhaust - helps you surive ganks or getting kills. You can use it after blind goes away when fighting with an heavy AD damage dealer.