Welcome to my AP/AS hybrid teemo. It's more oriented on AP but with AS about 1.7 and then about 1.5 it can be called hybrid. This build will give you awesome firepower with your basic attacks as well as bliding dart dealing 600 dmg. This build is good for team support with your shrooms but also you are pretty good damage dealer and with lich bane, killer as well.

My choices
Flash is always a good choice for Teemo. It provides a good escape mechanic, as well as being able to flash in/out quickly to shoot that last dart that will land you a kill on the runner.
I use ignite mainly because my poisons are quite deadly.It means that someone who hasn't got so much hp can be killed easily by me but combining flash, ignite and then move quick to run is a 100% kill

Viable Choices
Teleport is another decent spell for Teemo. This will allow him to get to lane quickly since you should be soloing anyways, as well as set up mushrooms in the jungles and along lanes. KEEP IN MIND YOU CAN TELEPORT TO YOUR MUSHROOMS! This is great for ganks.

Ghost is also a great choice on Teemo. Combined with his move quick, he can quickly move across the map for ganks, and it helps him escape from bad situations or chase down that enemy with low hp.

Decent choices
Exhaust is never a bad choice for DPS. This will help you with your 1v1's and your runners, however I think there are better choices for Teemo.
Heal is better for players new to Teemo or new to the game in general. Using heal at very low hp will catch the over-extending enemy off guard and may land you a kill. However, this is not the best choice for Teemo.

Cleanse isn't a good choice. You would rather buy a mana potion in an early game than lose 1 summoner spell because you won't need so much mana.

Everything else is a no.

I take Bliding Dart first. It is very useful for harassment at the beginning of the game although most people prefer Toxic Shot. I think that Ignite can compensate it when going in for your first blood.

However, Toxic shot is awesome spell. With your ability power it takes very high damage, mostly in late game but when nicely farmed, also in about 20th minute.

Move quick is something like ghost. I take it on lvl 3 for the passive. Then I max it as the last spell because it is more or less needless to max it more.

Noxious Trap is your best spell. Late-game dmg (about 1105) is really awesome either for starting or ending team fights.You can start the team fight when enemies run through few of your mushrooms or you also can randomly hear "godlike" when somebody is running away with low hp. That's really an awesome feeling :D

I start with Boots of Speed, 2 Health potions and 1 Mana potion. This will help you to stay at lane for quite a long time because with boots of speed you have the movement speed you need to harass the enemies or to tackle or dodge their spells. In case you don't manage to do that, you have 2 health potions. Mana potion is for your bliding dart because you usually use that spell a lot.

Your second item is Sorcerer's shoes. This will give you magic penetration which is very useful for you.

Then you buy Malady. Malady is awesome thing for early game. It will give you attack speed and few AP for your future playing. This item will be sold and replaced by Void Staff in very late.

Nashor's Tooth is item made just for you. It gives you simply everything you need.

Rabadon's Deathcap is your major item. Gives you needed AP to finally do something and help your team. Also it is very important to build it because of your next item.

Lich Bane is item that will help you kill everyone in 3 shots. You simply shoot Bliding dart, then auto-attack and you will deal around 1000 dmg. You can also put some mushroom and shoot again (again 500 dmg + ) Simply the best item.
(Also it gives you movement speed which you need)

Rylai's Crystal Scepter is item that you need to survive. This will give you additional 80 ability power + 500 Health which helps you to survive. Also gives you a slowing effect for your spells. Simply awesome.

Your last item can be bought but I prefer it. You will replace your Malady which is not very useful in late game with Void Staff that helps you kill even more with everything you have.

In brief, all you can hear with these items is "Godlike".

Basic Tips:

-Last hitting minions is important! Try not to push your lane too much or you will leave yourself vulnerable to ganks.

-Do not be afraid to use shrooms on a large wave of minions coming at you. This will help you kill then in a short time.

-Keep enemies afraid and away from you. Harass them with Bliding darts and poisons. Place mushrooms mostly on places such as grasses at the beginning to prevent ganks. In later game place mushrooms on an usually used routes. You will later realize where it is.

- working on it

Pros:
- speed
- damage support for your team
- ward support
- last-hitter

Cons:
- vulnerable (low life and resists)
- usually focused
- not very good at solo in the beginning

I've chosen 21/0/9 giving me the most AP as I it can.
Another possibility is to put more masteries into Utility but I prefer 21/0/9.

I recommend this build for everyone who likes to have fun but also kill everyone in 3 shots.
Last but not least you are very helpful for your team so don't hesitate to try this build!

Thank you for checking out my build! Please vote and comment. Do not hesitate to add suggestions.