You go fast and harass their points. Don't worry about dying, but try to run away if the enemy shows up. Force them to always be on the lookout for where you will show up next.

Pay attention to your build prices and only intentionally go back when you have the gold for the next item.

Max your stealth (Q) first and your slow (W) second. Stealth through the jungle, use the move speed shrines, and capture points ASAP. Try to time your captures with their pushes, or when the rest of us are dying/dead. Don't be afraid to use Revive whenever it is off cooldown.

Max his Move Quick (W) ability first, and his poison (E) second. Teemo will stealth if he stands still for a few seconds, but make sure you are not too close to a point, the turrets should still see you. You should be pretty fast with your basic attacks, don't be afraid to engage a lone champ with low health. Try capturing a point, then hiding near it to see if a low health champ comes to get it back or defend it.

Max his Overdrive (W) first and his Power Fist (E) second. Use his power fist to knock champions up to give you time to escape. He's a little beefier that the other two, but most champs will still melt you.