Well I have played Teemo an awful lot in 3v3 and I have seen some in what i consider terrible builds and ideas, this is my personal build to make Teemo into the king of 3v3. your team will love you, the enemy team will rage.

For this Teemo

Pros

-Extreme shroom damage

-You will own the jungle

-You can get kills without even being there

-Every shot and ability murders people

Cons

-Often focused

-It is dangerous to go alone

-Can get a bad start and will often cause you a long painful game

Glyphs: well Duh Teemo is AP no, hes not ad, not at all shut up.

Seal: Mana regen: Well laying a lot of shrooms is mana pricy, so having some isnt bad. Health: Every little bit helps the weak health Teemo.

Marks: Magic penetration, for obvious reasons.

Pretty simple, more damage makes people cry/rage.

Boots and dagger: Starting with your E you want to get as many shots as possible this will help you in a level 1 fight and to farm more than taking your Q first.

Stinger -> Nashor's tooth: This item is very effective as it gives cool down reduction, attack speed, and ability power. I always go with the stinger first because of the CDR and Attack speed.

Sorc shoes: Make everything hurt that much more, each less magic resistance they have is closer to true damage.

Black fire torch: The real bite behind a shroom, some people prefer to rush wooglets or a crystal scepter but in every game i have ever played with this build, BFT is what keeps them out of your jungle(or theirs). If I am having money troubles i get the pick first if not than the mask.

Void Staff: Ability power and more of that sexy magic pen.

Wooglets: by now your shrooms are already very potent but after this not only will they be potent they will be down right rude. Not to mention your blind and poison shot.

Crystal Scepter: This is a great item for when someone does step on a shroom say if you get aced and they make a mad dash to get your altars or whatnot this will keep em slow and burning with the torch. Not to mention the ability power and health.

Potions: Items that don't take up slots but give bonuses, not a bad idea between items or at end.

Wait till at least your stinger preferably Nashor's tooth to jungle, and your Q blind the biggest and shoot it down first than deal with rest, pretty simple.

Against lane Creeps, try to last hit but really it shouldn't take more than two shots each. If you have a spare shroom and a big wave is coming put it in the middle and let em chase the shroom will eat them.

You are Teemo it is your job to secure your side of the map, at first anyway. You also provide an invaluable escape service, most people will stop chasing you after the first shroom but I have seen people die chasing as a teammate or myself runs em through 5 or more shrooms. Keep in mind that the poison DOT does NOT stack each new shroom damages and refreshes it, that initial damage is potent though so you can put them close by but putting multiple on top of each other will only hurt a lot up front.
Shroom up the jungle Below i put the dots where I put shrooms, in three handy colors.

Green: Always put these down, replace if stepped on.
Orange: Only if you are paranoid or if they have pushed you back pre shroomage and they still venture into your jungle.
Red: This is their jungle PUNISH THEM AND OWN IT!

Purple Team:
Blue Team:

Why E at level 1? You will do more damage than the blind in terms of base damage and damage over time. Also it will help you get your CS up early and help you level faster. You max this first so you can farm easy and hurt champions easy.

Q Is your second to max, some people say W to move faster is better, but in my opinion with this build you can sit wait for them to hit a shroom and blind the hell out of them than tear em apart with basic attacks.

W last because you should only need to run down with it.

R when you can because, well that is the point of this guide.

Alright so some spells to consider

Everything other than these is Wrong.

Ghost: Good for running down your enemies goes well with W, both together will get you that kill or save your tiny furry butt to shroom another day.

Flash: I suppose it is alright but I find ghost better for him.

Ignite: You already do a bunch of Dot, why not some True Dot to that, plus less healing win/win.

So in short: rush level 6, punish anyone for going into the jungle, make sure you tell the team to use your shrooms as escape paths, and you should be the reason you win every time. Oh also watch out for oracles...those jerks.

Thanks for reading.