Hello, welcome to my Teemo build: I haz Bonus DMG. The build is titled like this becouse all the items you will have will give passives which will give you more damage, instead of buying attack damage.

If you choose to downvote, please tell me why in a PM or in a comment.

Pros:
- Very nice damage per dart
- Nice last hitting minions
- Noxious Trap can be a ward and warner
- Deals nice damage overtime becouse of Toxic Shot.

Cons:
- Very squishy
- Often targeted

I chose for the runes:

- Greater Mark of Ability Power (0.59 ability power each)
- Greater Seal of Ability Power (0.59 ability power each)
- Greater Glyph of Ability Power (0.99 ability power each)
- Greater Quintessence of Ability Power (4.95 ability power each)

This will give you a total of 34.38 ability power at the beginning of the match, which will allow you to get more damage out of your poison in the beginning of the match.

In the Attack Tree, I chose Mental Force , Blast and Archmage because they grant more Ability Power, which will stack nicely with our ability power runes.
With Arcane Knowledge you recieve more magic penetration, which will result in even more magic damage.
Then Havoc and Executioner will cause you to hit more with normal damage, and the Sorchery to spam your Blinding Dart more often.

In the Utility Tree, I chose Expanded Mind and Meditation to give you that extra amount of mana which will cause you to be able to spam your Blinding Dart easier.
Then I chose Summoners Insight to lower the cooldown on Flash, and also Swiftness just to make Teemo even more faster.

I chose for the items:

Berserker's Greaves: These boots won't give you only movement speed, but you will also recieve 25% attack speed, which will cause you to get that extra amount of attack speed in the beginning.

Wit's End: This item will give you 40% attack speed and 30 magic resist and has 2 passives: You will recieve 5 magic resist per stack (with a maximum from 4 stacks) for 5 seconds and you will recieve 43 bonus damage every basic attack. This will give you more damage early game, without purchasing an attack damage item.

Sword of the Divine: This item will grant you 60% attack speed! This sword has a nice passive: Every fourth basic attack, you will deal another 100 damage on top of your damage. With your nice attack speed that you now have, you will recieve this bonus quite often, which will cause your damage to be even bigger. It also has an active: when you activate it, your attacks cannot be dodged and you will recieve 30 armour penetration for 8 seconds. This active has a 40 second cooldown.

Madred's Bloodrazor: This item will give you 25 armour, 30 attack damage and 40% attack speed. Not only will it give you more base damage and another boost of attack speed, its' passive gives you the ability to hit 4% of your opponents' maximum health every time you do a basic attack. This will grant you to do even more damage.

Hextech Gunblade: This item will grant you 40 attack damage and 70 ability power, but it also gives you 15% lifesteal and 20% spellvamp. This will be an awesome thing for Teemo, becouse now he can sustain more in lane and in fights, becouse his life will be regained through his basic attacks and his Toxic Shot. It also has an active, which will damage the target for 300 damage and slows it with 50% for 3 seconds.

Tiamat: This item will give you another 50 attack damage, 15 health and 5 mana regen. This will, together with Hextech Gunblade, cause Teemo to stay alive in fights. It also causes 35% splash damage with every basic attack due it's passive.

Blinding Dart: This ability will cause an opponent to miss every basic attack he does. Together with that, it will cause a good amount of damage. You should try to max this ability as second.

Move Quick: This ability will cause you to passively have increased movement speed untill attacked by a turret or champion. If that's the case, it will restore in 5 seconds. If you use this ability, the % that's increased will be doubled for 3 seconds. You should try to max this ability out as last, becouse it isn't that important to have this ability at higher level. Make sure you choose it at level 3 though.

Toxic Shot: Causes an opponent to be poisoned for 4 seconds every time you hit him with a basic attack. The damage won't stack, but the duration will refresh every time you hit him. You should try to max this ability out as soon as possible, becouse it is an important part of your damage.

Noxious Trap: This will lay down a mushroom, which will be triggered after an opponent walks over it, causing an amount of damage and slowing the person for 4 seconds. The trap will last 10 minutes, after that time, they will vanish. Make sure to max this ability as soon as possible, which means at level 6, 11 and 16.

Most likely Summoner Spells to pick:

Flash: always good for escaping in fights, if your Move Quick isn't enough.

Ignite: when you just can reach your opponent, Ignite will do the last amount of damage in combination with your Toxic Shot.

Exhaust: when your opponent tries to escape, you will use Exhaust on him and you will take him down with your attack speed.

Possible Summoner Spells:

Ghost: You'll be able to run faster, but because of the high movement speed of Teemo and his Move Quick ability, you'll probably run fast enough.

Cleanse: This is another one to flee, if an opponent has a slow, you can get away easier if you clear yourself from effects. If this is not the case, Cleanse is kind of useless.

Summoner spells NOT to pick:

Heal, Clarity, Promote, Revive, Teleport and all the others. These won't be good to play with, becouse it's just not required to pick them.