Teemo is no doubt one of the best ranged champions in the game. I have played LoL since 2007 and all the time i play almost exclusively teemo.

PROS

does lots of damage at lvl 1 ( 2X more than ezreal)
does mixed damage
can stealth
is pretty fast with his

Move Quick ability

CONS

is kinda fragile
does less damage vs. turrets

Passive:
Camouflage
Can be very amazing when used properly. I, for example go fast to mid and stealth there in the middle of lane. when somebody like Ashe comes, you can troll him by shooting him with bursty magic and physical damage
Blinding Dart
This shouldn't be your main nuke spell, although it is really useful. the main purpose of this spell is to prevent enemies from killing you with basic attacks while you do your "job"
Move Quick
Great escape tactic, as my brother says "Integrated Ghost". It has saved my life many times, and is also useful when chasing low-health enemies
Toxic Shot
This is your main skill. It is used as your main nuke spell. Also contains the poison effect, which makes escaping enemies die. As this build guide is for attack speed teemo, in combination with Runaan's Hurricane and Wit's End makes teemo deadlier than death itself.
Noxious Trap
I use this ability only as an alternative for sight ward. it can still be pretty useful for detecting ganks, but since you want to focus on damage, upgrade rather Toxic Shot and Blinding Dart

ABILITIES YOU DO WANT TO USE
Ignite - what is worse than enemy with about 5 HP behind tower laughing at you?
Exhaust - if you don´t want people to escape, this is your best choice
Heal - A life- saver, if you are ignited or so
ABILITIES YOU MAY CONSIDER
Flash - Can be really useful when you are being ganked, but it's not necessary if you pay attention
Teleport - Can spare your time when travelling after a recall or death
Revive - Can spare you lots of time (and a nexus) if you die
Cleanse - If those slows are too nasty, just press "F"...
Useless and junk abilities
Ghost - Useless, since teemo has the Move Quick ability
Barrier - the damage prevented is not big, and you have heal...
Smite - you are no jungler...
Only N00BS use this one:
Clarity - Totally useless since teemo's main nuke costs NO MANA!
I generally use those:
Ignite
Heal

At level 1, your main goal is to troll other ranged enemies with camouflage and Toxic Shot by standing in the middle of a lane while in stealth and attacking enemy champions within range.
BEWARE OF CREEPS- if they get within basic attack range, unstealthed teemo will start auto-attacking them. when you get stealthed, teemo doesn't attack creeps anymore
As the game continues, you want to get Runaan's Hurricane and Wit's End as fast as possible, then build either for attack speed, AD or AP (AD and AP builds are published here)
At the late game, you need to get as much of either AP or AD as possible, high armor and magic resists of enemies make doing high damage output harder. For AP, the combination of Void Staff, Sorcerer's Shoes and two Rabadon's Deathcap looks like your best bet.

I play teemo as a mix of AP and attack speed. At first, i rush to buy Runaan's Hurricane as fast as possible and then the same with Wit's End. after that, i either buy 4 Rabadon's Deathcap or a Void Staff, Sorcerer's Shoes and 2X Rabadon's Deathcap.
I tried AD teemo only once or twice, but since most players got more Armor than magic resist, it wasn't so terrifying.
Well, this is end for now
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