Let me preface this by saying that Jeff's answer is great, and this is merely an addendum.
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.
Boots first. This should go without saying against any skillshot champ, but it's absolutely vital for getting away from Swain stun.
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).
Farm farm farm. When Swain leaves the lane, push and push hard.