This is the Teemo build that I've used since I laid finger on this little guy. This build is great as it can take down tanks like Cho'Gath, Rammus, and Shen as well as destroy squishy champs like Ezreal, Ashe, and Annie. This build is extremely micro intensive as you will have literally be the squishiest on your team.

The way I have my runes set up for this build is flat Attack Speed. You will have about .950 atk spd at level 1. This combined with your Toxic Shot ability is sure to rip apart any champion you're laning against.

The masteries I have set up for this build is a 9/21/0 build. Since you will be squishy, you need the extra defense from the masteries. It'll keep you alive during harass and narrow escapes. Trust me.

I take Toxic Shot first. This is your main damage output from early to mid game. Max this out first. Level 2 I take Blinding Dart. This will give you the edge when you want to harass hard. level 3 I take another point into Toxic Shot and then level 4 you get your Move Quick. Activate it only when you're getting chased by ganks or to escape from dying.

For this build, I like to take Flash and Ignite. Teemo is a quick little guy so and he can stealth. Flash is used to either escape from death or to catch up to a sure kill. Ignite just works so well with poison.

If you want to run an even safer Teemo, take Ghost and Flash. This will help you secure a safe return home.

Another set of spells I used to run: Flash and Exhaust. This is mainly for 1 v 1 purposes but it works well in team fights too.

Pros
-Rips early game.
-Rips mid game
-Rips late game
-Very fun to play this build
-Micro Intensive

Cons
-Very squishy through-out
-Not for everyone

Always last hit. Always. Farming is key to winning in any game. Since you have Toxic Shot early, your harass is good enough to keep melee units back behind their own minions. You just pick off the dying minions while they cower in the back. Don't play aggressive unless you know you can get away with dealing more damage to the enemy champion than you can take from their counter and minion attacks. Again, last hit.

This is important. Even if you have all the runes and all the masteries set-up you still have to know exactly how to play this type of Teemo. I've seen people play Teemo full AP build. In my opinion, those don't do so well. I've seen Teemos go AD and those do okay but all they do is stand there and attack. That's not so fun. This build is micro intensive. That means you have to be doing a copious amount of kiting and moving in and out of bushes. Here's how I play Teemo.

-Early game-
It doesn't matter which lane you take. If you play right, you will dominate. If I'm mid, I grab my book and head in the middle. Remember, Teemo can Stealth so use that to your advantage. Hide there until the minions come. You will be in the middle of the battle between minions. Depending on who you're up against you can get away with certain things. Mages like Brand, Lux, Malzahar, and LeBlanc are the easiest to bully. They depend on their skills. Once you see them use a skill, go in for a quick two shot harass. The flat Attack Speed Runes will help out. By level 3 you should be a little below full health with a pot and they should be either half health or less than full with no pot. If you're facing a ranged character, check who has the higher attack speed. If it's you, than you can get away with a two shot harass after every 1 minion kill. After you get Blinding Shot, harassment shouldn't be a problem. Just remember to keep moving. If you're laning against someone who has a skill shot, always strafe. By level 3 or 4 you should pick up first blood or at least a kill. Go back to base and buy level 1 shoes and a dagger or two. When you get back in lane, your opponent should either be mad enough to be stupid and try to kill you back or be so passive that they stay under their tower. This is when you play your smartest. If they're passive, farm. Only harass when they try to attack your minions. If they're aggressive, pull them into your minions and then attack them with Blinding Dart first. Use your stealth often. Since they can't see you they will either call MIA and try to farm and then you can kill them or they'll be cowering. Use this to gank.
*Ganking*
By level 6, ganking should be something you do often. Push your lane and gank. Always go to the lane that is being pushed by the opposing team. Set up a few shrooms in the river and head towards the aforementioned lanes. Pick off the squishiest. Even if you don't get a kill at least they will have wasted a summoner spell or two. Go back to mid and farm some more.
-Mid Game-
By this time, you should have a Malady and your Berserker's. Great. Now you'll be attacking so fast that no one can stop you. Maybe. When you have a free shroom, use it to keep an eye on the opposing jungle's Blue and Red buff. You might want to put all of your shrooms in their jungle. If they can't maneuver in their own jungle, they won't be able to farm neutral minions correctly and they'll be lower health when they get back to lane or for a gank. Sometimes I like to stealth myself near a shroom and wait 30 seconds to see if any champion shows up. If they do step on the shroom, wait for the slow to exalt and then shoot them with Blinding Dart and 4 shots. Then run. It doesn't matter if you kill them. This is just to get under their skin. They have to continuously go back to base to heal and they can't farm because of you! During team fights, try to stay outside of the current battle. Stealth yourself and let your tank take the damage. Let your mages do the nukes and your melee's to help lower the enemies. Your job with this build is to blind the AD damage dealer and kill the mages and stragglers. The reason why shrooms in the opponent's jungle is good is because anyone with low enough health will die from your shrooms if they hide in a bush that has one. Aim for big hitters like Ashe, Cait, Talon, and Shaco. Blind them, run and if they follow you, they're good as dead. Your attack speed plus the continuous damage from Malady, Toxic Shot, and Last Whisper will drop them fast. Even if they start to run away, your shrooms can still kill them. If they don't it's fine. They'll either be so low that they can't help or they'll come back and you just kill them then.
-Late Game-
By now, you should have all your items and your mushrooms are wild in their jungle. There's literally nothing left to do except run rampant on their feelings. I usually just stay stealthed in obscure locations within the enemy jungle. When an opponent comes, you can kill them within 10 seconds. Blind and then fire away. If it's a melee character, run into a bush shoot from their, then run out and shoot from there. Then run away as if you're scared. Stealth and then stalk them some more. Plant mushrooms all the time. Steal blue all the time. And remember to keep moving.