i know as you look at this all you're gonna say is "WHAT THE FUNK... NOOOOOOOOOOOOB BUILD" but trust me, ive been using this build for a while now in ranked games and been getting marvelous results. my main concern is that, if you are new at playing Teemo, please, please, please do not use this build.
if, however, you are good at Teemo, this build is for you!
remember this "always on your toes" as we go through all the phases of the build.
Fortify is just there to help your team... you can always swap it for Teleport to bd inhibs. land on Noxious Trap in brush to gank etc...

you will ks a lot due to ur Toxic Shot
so expect a lot of "DUDE WTFunk"

Please vote if you try it...dont if you dont ;)

Pros:
EARLY GAME:
- Blinding Dart does marvels to enemies.
- Noxious Trap "bro shrooms" (as i keep trolling enemies) help your mates more and more as you level.

LATE GAME:
- 3 hit kills by end game
- said bro shrooms put at critical areas in jungle will ALWAYS get you a kill from escaping enemies.
- after getting this build blinding darts does so much damage and crit.

ALL THROUGH:
- OMG HE'S SO CUTE (oh you know it!)

CONS
- this champ is super squishy. "always on your toes" means you dont just stand there and farm... right click madly so ur never just standing there farming (focus on last hits).
- if you are doing well early game, YOU...WILL...GET...FOCUSED.
- if Flash is in CD you have no GTFO skill, so instead of running (if you're dead either way) turn and inflict some damage till a mate comes by.

I tend to max out my def masteries to add some survivability to this squishy as funk champ!
9 on the damage rather than the ability tree is just so that late games your runes would boost you (check runes area down below)
i got this tree set up from another build i used to use found here get me teemo over here with a blowgun by ferrovial

that was the best build i've used, but im more happy with mine now :p (Original Poster's build is awesome and all, and Ferrovial thanks for helping me reach this build i now call mine :p)

now the runes, where im sure you'll go " OMG YOU NOOOOB WTFUNK IS THIS"

reasons:
Greater Seal of Attack Damage and Greater Quintessence of Desolation gives me more AD early on (plus the ap items for utter PWNAGE)
Greater Mark of Critical Damage for late game PWNAGE (full ap/ad build)
Greater Glyph of Scaling Magic Resist well... at level 10 Greater Glyph of Scaling Magic Resist runes will give more resistance than Greater Glyph of Magic Resist... that... :p
Greater Glyph of Scaling Magic Resist + Evasion and Nimbleness from masteries will allow you to "be ok" through out keeping in mind you are destroying your right click mouse button "always on your toes"

as you see, no pots... be smart... im not gonna say "buy this now" cause you should probably keep 2 health pot and 2 mana pot with you at all times... ok? no? hmmm... nvm... moving on

i tend to go for AP first to maximize power of my bro shrooms all the way.
if you're having trouble with GTFO buy Boots as your second item then finish off Malady.
AP PART
- Malady gives you awesome speed from the 2 Dagger early on + some AP from Amplifying Tome to boost your Blinding Dart and poison shot as well as effectiveness off noxious traps
-tbh, Berserker's Greaves, just for ATS i tend to switch it up with Mercury's Treads if enemies focus me with stuns, slows, etc. TENACITY HELPS (if you are really good at moving all the time go for Berserker's Greaves, this is just a tip)
-i usually go for Wit's End next to give me all the AS from Recurve Bow i need for the first half of the game.
- Rabadon's Deathcap... so much ap that your Toxic Shot, Blinding Dart, Toxic Shot combo (auto attack, Blinding Dart,auto attack) will inflict so much damage you'll be like "/all trolololol, look at meeeee" (i know you dont press Toxic Shot but for sakes of it i call it that. pronounced IKKY)(im not 12... shocker huh?)

AD PART
-always always start with the B. F. Sword this way your Toxic Shot, Blinding Dart, Toxic Shot combo (as stated above) will do more and more damage) then work some Cloak of Agility, Pickaxe, Infinity Edge.... after Infinity Edge you'll be doing mad amount of AP+AD(crit included) damage you'll be destroying squishy enemies in 3-5 hits MAX always remember Toxic Shot, Blinding Dart, Toxic Shot combo.
- Phantom Dancer just adds a lot of ats and ADcrit.
- now Bloodthirster... with that speed damage crit and life steal... "DUUUUUUUUUUUUUDE that teemo is so op!" yeah... trolled and focused a lot by now... so stick behind the tank on ur team.

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TIP: sometimes after i finish my build and find some money on my hand... i sell Berserker's Greaves or Mercury's Treads and get another Phantom Dancer, which gives you movement speed too, so 2 Phantom Dancer = more crit+ats and a lot of movement speed to ditch the boots.

you will be focused
you are squishy
you do so much AP AD that its really fun to play this build
you will die a lot if you dont move all the time
dont rely on your passive as a get away
Flash + Move Quick will help you GTFO before you die.
really squishy
really squishy
really squishy
so much POWER on that dude
last hits is the way
blue is your friend (golem)
grab dragon with your mates all the time as this build is expensive
PLAY SAFE.
you need your team mates, dont chase unless its for an ACE
always stay behind team mates in fights
at level 6 you should be dropping Noxious Trap everywhere like crazy
and oh... "always on your toes"

i will upload some videos of how to play this build

and let me know what you think... again... i dont expect this to work for every one it does for me... so i thought id share it.
before you comment (positive or negative) try it with bots for all i care ;)
also, remarks are more than welcome, and will surely help me figure out some stuff to add to help me and you with this build