So, this is basically my Teemo build. My first one too :D. This is my way that works. So, I hope you get the chance to try it before you derate it. Thanks.

Pros

-Amazing carry
-Great farmer
-Good damage output
-One of the amazing tank killers
-Great pusher
-Free 5 minute wards unless detonated

Cons

-Squish squish squish!
-Oracle/Vision Wards can take his shrooms down
-Low HP
-Smallest range for a carry
-Focused in fights

For summoner spells, i take Ignite and Flash. Ignite is for that extra damage to take down the champ when they're low. It also helps to reduce effectiveness of healing of characters.

You could also take exhaust, ghost(which i don't recommend, or maybe even teleport if you want to suprise attack by teleporting to a mushroom.

So I personally go with magic penetration marks, cooldown reduction seals, magic penetration glyphs, and movement speed quints. So I get magic pen because it helps take down tanks. Madreds does % health in magic damage so it will help with taking down tanks and also killing champs faster. CD reduction is self-explanatory. More shrooms, move quick is replenished faster. I get movement speed because even though teemo has his passive W, he might be too slow for getaways if his W is on cooldown, so a little more movement speed helps.

I build 16/0/14 taking AP, CD reduction, attackspeed and magic and armor penetration for offensive, and max mana increase, health/mana regen, time spent dead, and experience for utility.

Early Game
I start out with a regrowth pendant and a health potion. Always try to harass the opponent with one hit. Hitting them gives them the poisoned status and they lose more hp. Also remember to last hit minions because gold is very important. Continue farming and harassing until you get about 2000 gold. When you go back for hopefully the first time, grab sorcerer shoes and a philosopher's stone.

Mid Game
Begin to start building towards a Malady and a Vampiric Scepter. Mid game you should have some shrooms planted in the brush around your lane to be able to get away from getting ganked. Also, you should ward the dragon so your team can go steal it from them and possibly get a kill. At this time you can start ganking other lanes and getting fed. If you aren't that well fed continue farming and wait for someone to start ganking. Getting kills and assists are important for Teemo because he is a carry.

Late Gane
At around this time, you should be close to getting a Frozen Mallet or Madreds Bloodrazor. You should be pretty well fed and if your team played well, a few turrets should be down. Start warding Barons and try to backdoor some. You can also jungle for Golem Buff to make more shrooms. When team fights occur, you should stay back and get the champs that are running away. Then, take down the tank after all the squishies are dead. You can also backdoor a few turrets. If things go well, you should be able to win quickly or they will surrender.

Have fun :D