Full Build (in roughly this order):
Sorceror's Shoes, Nashor's Tooth, Liandry's Torment, Rabadon's Deathcap, Runaan's Hurricane, Void Staff

Now I know that a lot of people are going to say, "NO, NEVER EVER GET A RUNAAN'S!!!111!!11!!!"
To them I say, "nyeh."
Runaan's is quite possibly the most effective on-hit item in this game, and Teemo has an incredible on-hit ability. With his Toxic Shot (E), I can apply heavy DoT to three targets at once, which makes for quick waveclears (even when two or three waves have built up) and makes me able to 1v2 or 1v3.
Sometimes I'll hold off on turning
into
or my
into
while I get
.
The main reason I don't have a
is that I always forget to use its active. It does provide a lot of AP, but I feel that the more frequent auto-attack hits in my build balances it out. I also do not build attack damage or life-steal on him. He does plenty of magic damage on hit, and you should be hiding behind minions or running away (to flank them from the jungle) to avoid taking damage.
I also avoid
because my AP items provide more AP, and Teemo needs lots of attack speed to use his E well.
A note on clearing waves: When you have a few levels in E, be sure to switch targets with each auto-attack. Poisoning several targets will clear the wave faster than attacking only one minion at a time.
For abilities, I start with a couple levels in Q for poking. Then I max out E, then Q, and W last. R>E>Q>W
Q is very useful when going against AD champions because the blind nullifies their main method of dealing damage, and then I can get a few shots off to apply tons of poison damage, which usually kills squishies or leaves tanks at low health and much easier to kill.
A key note on your mushroom traps: Always set them out/keep R on cooldown. If you have more than one in your inventory, you're throwing away potential damage and map vision. Use 'shrooms to keep sight in bushes, watch jungle lanes, provide escape paths for yourself, and provide a damaging buffer for those who try to get close.
I usually play Teemo in bot lane as either AP marksman or support (AP and AD damage-dealers!), though he should work fine in top or mid.
Edit: I just crunched some numbers, and if I did it right,
with
does ~26.48% damage on just the %HP DoT from Liandry's stacked from the DoT on Toxic Shot (E). Add in
, and it jumps to ~46.84% damage, again, just the DoT.
Based on this, I may trade out either
or
to get
.
Edit 2: I just saw some other threads that discuss stacking DoT. It seems that Liandry's might just reset its DoT timer on each tick from Toxic Shot. In this case, the damage is ~13% without Rylai's and ~24% with.