When playing Teemo top I often get "counter" picked by Swain. I've had trouble playing against Swain because of his high damage and not being able to harass him down like most other ad bruiser tops. Any tips on how to play against him?
There are three basic tips for laning against Swain with Teemo. You have to understand, however, that just based on the match-up this will probably be a fairly passive/defensive lane for Teemo.
If you can do all three of these well, you can stay competitive in top lane as Teemo (regardless of the Teemo build you're choosing to go with).
Let me preface this by saying that Jeff's answer is great, and this is merely an addendum.
1) You're probably not going to kill Swain. By the time you get enough items to be annoying-Teemo, Swain will probably have his six. At that point, you just can't stop him.
2) Boots first. This should go without saying against any skillshot champ, but it's absolutely vital for getting away from Swain stun.
3) Get an early null-magic mantle. You're going to be in this lane for the long-haul, and you'll probably want merc treads (unless the rest of his team has absolutely zero cc, in which case you'll build it into something else. Like Wit's End).
4) Farm farm farm. When Swain leaves the lane, push and push hard.