Looking at the builds on mobafire I saw none to my liking. There was a lot of AP Teemo, which I really don't like. I find Teemo was meant to be an AD because with a lot of attack speed his pipe is an automatic. Another thing was when I tried them out, I found that I kept getting stuck with low health. With no armor and few health these builds weren't to my liking. Therefore I thought of Life Steal Teemo. With Bloodthirsters that give 70 AD and 12% life steak, it's a broken combo. Basically full build you can solo the enemy team, you will come out with full health, an ace and hopefully a surrender. Using my own build I have myself gotten many Pentas. This build offers a different view of Teemo, a tanky AD carry. Sometimes you can even be the one to initiate a team fight. There's nothing to be afraid of if you have Life Steal.

BTW COMMENT ON HOW YOU DID WITH THE BUILD

The main items are, Hurricane, Shiv and Bloodthirsters. You can swap out the last item for, warmog's, guardian or phantom dancer. The reason for warmog is because by level 18 you will have nearly 3k hp, plus the life steal of 3 bloodthirsters, so basically your indestructible. Who wouldn't add in a guardian angel on Teemo? With life steal the effect of guardian angel (revives you with 30% of you maximum health) the moment you come back and the whole team is waiting around your "dead" body, you will easily get a Penta. The moment you will start attacking them your health will go up as theirs goes down. Last but not least is a Phantom Dancer, this is mainly just so you can life steal faster, but I would recommend guardian or warmog.

Pros:
-Indestructible full build
-Has astonishing Life Steal speed
-Able to be tanky
-Can fight the enemy team
Cons:
-Squishy early game
-His weakness is cc's, because if he's knocked u or stuned he can't attack so no Life Steal
-Relies on items

Remember your the AD carry so you need to be hungry and feed off the other team. You have to carry the team in kills, you need to be that guy that everyone on the other team hates. At the beginning your going to have to get some kills but don't expect to get 10 before your done the laning phase. Also your ranged so you can still attack if they're turret hugging, just use your Q at maximum range from the enemy champ and move a few steps and you could keep poking. Late game is when you have to step up. Your team is counting on you, don't screw it up.