So as first I must say that English isn't my native language, but I will try write as good as I can... This is my first guide, and it's for most annoying champion ever Teemo The swift scout. I have played with Teemo around 500 games, and every game I improved this build to be stronger and decrease Teemo's cons and it ended like this... Hope your enemies will get rage like Tryndamere. ;)

Guide is still in construction.

So here I will explain why this items ...
Liandry's Torment It will give your Noxious Trap nice dmg and some M. penetration. Oh and it works beautifully with your Noxious Trap when enemy gets slowed, will deal extra dmg.
Morellonomicon When your enemy is under 40% of hp he will get grievous wound from your spells it's also good on Noxious Trap cause u have bigger chance to get kill... And also it will give you some extra mana regeneration
Zephyr You will dont't need any boots and you get some nice atc. speed with cooldown reduction.
Lich Bane It will give you some nice dmg on Q+base attack combo, so you will have nice poke.
Rabadon's Deathcap It will give you nice AP...
Runaan's Hurricane Will grant you even bigger atc. speed, it's great thing for you into teamfights.

As spells I support:

1. Teleport: It's nearly best spell for Teemo, cause you can easily gang any lane, save your allies, and also as I will write in next chapters, get kills/buffs. It can also save many turrets...
2. Ignite: One of best spells for Teemo cause with your ignite, grievous wound from Morellonomicon, burning from Liandry's Torment, and your Toxic Shot passive you will always get kill no-one can escape you with small hp, even if he have Barrier or Heal ...
3. Flash: It's good for escaping, and getting kills (aggresive flash for kill) but I don't prefer this for Teemo cause your passive+ Ignite+some next things will often give you kill and while escaping you are almost fast as Master Yi so you really don't need it. But if you don't like Teleport this is best spell instead of him ...

Teemo is good in one team with:

Blitzcrank Cause he can Rocket Grab enemy into your Noxious Trap ...
Cassiopeia Many poisons ...
Volibear He can tank you anything ...

I have only few advices for u, and there they are:

1. At lvl 6 start placing "gifts" for enemy jungler on their red, blue (btw on what side of map you are), wolfs etc.

2. Don't place Noxious Trap into bushes, cause everyone will wait them here... Instead, place them next to bushes, and into thin places.

3. Until you build Zephyr , you aren't strong in close fights.

4. With spell Teleport you can port to Noxious Trap next to the enemy jungler, or dying enemy and get kill/buff, sometimes both. ;)

5:

Always when someone buys oracle, say your team to hunt him down as soon as possible.

6. On this type of Teemo is good to place some Noxious Trap on 1 location and camp here, but watch your lvl and don't camp long time on 1 place, cause u will lose XP/Gold and they will avoid this place ...

Pros:

Free wards for your team
Really big poke
You can easily escape
You can get buffs and kills also while standing on fountain
With my build Noxious Trap every 18 secs

Cons:

Easy counterable with oracle elixirSmall dmg at start
Often being focused in teamfights, cause no1 likes you
If your team have many AP champs and enemy build M. ressist you will have some problems

Teemo

is easiest champ to farm, even if you aren't good in last hitting like me, your poison often gets last hit... So this shouldn't be problem... ;)

While poking go like this: Blinding Dart + base attack and repeat...
While attacking, go like this: After every spell use base attack to maximalize dmg out put using of your Lich Bane ...

With Teemo team work isn't hard, just say them to teamfight/escape/fight in special places with more Noxious Trap and everything will be okey. Even if they will have oracle in teamfight they just cant avoid your Noxious Trap and you will win...
While doing Baron/dragon try to place Noxious Trap like red dots signalize on this picture.