teemo is meant to be played as a tanky mage dps backdoorer. in my build, you will be able to tank towers and 1v1 almost anyone (except udyr, xin zhao, ad sion, annie, veigar, brand, garen, vayne, talon, riven, tryndamere, master yi, nocturne and renekton)

during champ select, tell them that you're jungling teemo. pick teemo and lock in. take smite and say 'trust me, i know what im doing' NOTE: 50% of the time one of your team mate will dodge. change your summoners to teleport and flash last second. when you're ingame, lane with your top so its 2v1 at top. take boots and 3 potions. as soon as the game starts stealth in the brush closer to their tower. wait a bit and take first blood. with your 10 extra damage and -10 armour masteries, you should be able to take the top tower before 5 mins if the jungler doesnt come to gank. after you take the top tower, you should recall and get your boots of mobility + a few gold per 5 items. now you should roam around warding and helping your team.

once you get all 4 gold making items, save for a blood thirster. after that, get boots of swiftness, randuins omen and ionic spark.

explanation

boots of mobility - to roam faster
boots of swiftness - make it harder for them to catch you, even if you get hit you still run fast
randuins omen - they become slower when they auto attack you, also, this helps you backdoor towers. this item builds from heart of gold so this is the perfect item for this build
bloodthirster - lets you lifesteal your health back after backdooring a tower, allowing you to backdoor the next tower before without needing to recall
ionic spark - the attack speed helps you kill towers. this also helps you push lanes to kill towers.

be sure to buy oracles so you know if they can see you or not.

movement speed quints - make it harder for the other team to catch you
attack speed marks - attack speed most important stat on teemo after health (no health = dead)
attack speed glyphs - more attack speed better
armour seals - tank more tower hits

for masteries, take the +10 damage and -10 armour mastery

explanation

boots of mobility - to roam faster
boots of swiftness - make it harder for them to catch you, even if you get hit you still run fast
randuins omen - they become slower when they auto attack you, also, this helps you backdoor towers. this item builds from heart of gold so this is the perfect item for this build
bloodthirster - lets you lifesteal your health back after backdooring a tower, allowing you to backdoor the next tower before without needing to recall
ionic spark - the attack speed helps you kill towers. this also helps you push lanes to kill towers.

be sure to buy oracles so you know if they can see you or not.

help top lane kill tower earlier on in the game so you can roam the map and do important things to help your team win such as pushing towers in other lanes, ganking other lanes and stealing minions from your carry.