Hello everyone! This is my first guide on Mobafire.
I have been experimenting around with different builds with Teemo, and I believe that this is one that works fairly well because there are slows after slows (and with IBG, after even more slows).
I do realize that Rylai's and Frozen mallet don't stack, but there are still a lot of slows

I usually just take Doran's Ring but sometimes Corrupting Potion helps with some specific matchups that do a lot of damage early on (Zed, Irelia)

Runaan's Hurricane- You may ask, why Runaan's Hurricane. Well, you become a very effective splitpusher without having to use your shrooms to waveclear. Also, you can more easily spread your poison during teamfights
Nashor's Tooth- Since you will be building a lot of AP and AS, the added damage helps. Also the huge amount of AS and AP works well on Teemo. Synergizes will with Runaan's (Nashor's damage is on-hit, and the bolts from Runaan's applies that).
Hextech Gunblade- Great for survivability, especially at low health because you can autoattack and heal.
Rylai's Crystal Scepter- Every AA will give you a slow, which can let you stack up more damage on them. Also AP is great
Frozen Mallet- Health and slow is really nice to have, synergizes well with Runaans (on-hit slow)

Abyssal Mask- Lots of AP on the other team
Wit's End- AS + MR, again, lots of AP on other team
Rabadon's Deathcap- AP
Liandry's Torment-AP, health, and %HP burn- generally against tanks.
Void Staff- nice APen, a healthy amount of AP, but I prefer Liandry's
Zhonya's Hourglass- Armor+AP+Active is good for getting in teamfights, placing down mushrooms, then Zhonya's if that's your sort of thing. (I usually don't take it).
Guinsoo's Rageblade- AS + AP + a bit of AD is not bad. Teemo is, after all, an AS centered champ. It also synergizes well b/c of the extra on-hit damage.


Situational

Iceborn Gauntlet- More slows :D Q+ AA+AA+W+AA+AA+Shroom will be a lot of slows and IBG procs.
Ohmwrecker- Tower diving (very situational)
Morellonomicon- against healing champs
Guardian Angel- extra life
Rapid Firecannon- only get if you really feel like you want the extra range and crit.
Blade of the Ruined King- also heavy tanks, situational, AS and that bit of lifesteal is good too.
Hextech items- pretty much only one you might get is protobelt, but very situational
Armor- Heavy ad, Thornmail very unlikely, unless you have other armor its not that good b/c then you don't have enough AS/AP. Maybe against a very fed Yi.