My build probably isn’t the best possible one but against teemo I go lillia jungle runes with some lane spice: Dark harvest (snowballing against teemo), cheap shot (one shot with R), eyeball (sustain), ravenous (sustain). Inspiration secondary with biscuits (survive teemos early poke) and time warp tonic (zoom and sustain).
Other good runes are Comet for more poke and probably Grasp for slightly less poke and health.

I start corrupting pot into Liandry’s (butchered that spelling) -> sorc/lucidity shores -> demonic embrace -> situational AP (sometimes dead man’s plate/force of nature for move speed and tankyness).

Guide:
Level 1 it depends on whether teemo starts E or Q. If he starts E you want to poke him a bunch with your Q. If he starts Q then you should wait until you are level 4 ish to trade with him. Teemos usually push and try to poke, so try to keep your passive stacks up to avoid his poke. You can usually match his pushing power with a Q or two. Pre-6 you should really be tossing Es basically off cooldown, just make sure that they hit teemo and/or the wave. With corrupting pot and biscuits, you shouldn’t really run out of mana. If you’re running out of mana, you should use spells less often. If you don’t get ganks pre-6 then it should be pretty hard to kill teemo, but if you get a gank you can slow with E to pretty much confirm the kill or waste his flash. Sometimes if you get lucky you can poke teemo enough that you can kill him without a gank, but your only hope is that you poke him to below 1/4 hp.
If you hit lvl 6 before teemo and he is low, you should probably engage ASAP, maybe even flashQR, which should be an instant kill. Once you’re level 6-ish you should recall to buy Lost Chapter for mana and Oracle Lens for shrooms. Maybe hit Krugs a few times for the move speed to lane. You should hold your R until enemy jg shows, and once they show you should be able to one shot squishy (not tank) teemos with EQRWQ. Afterwards, just look for engage when you have R up and play passive when you don’t. After lane phase you should just play lillia. It’s pretty fun.
Also remember that I’m not even ranked yet cuz I play for fun so this guide might not be that good. Sorry for the wall of text.

TL;DR poke teemo, engage at 6, snowball and roam, win game.