If you're playing a ranged AP champion, constantly poke him whenever he comes up to farm. Auto attack his shield as it comes up so that to try and fight you would mean he'll eat all your abilities. Freeze the lane by your tower or halfway up since that means he'll have to risk himself to ganks.
As for his windwall, you can easily bait it by faking an all in. Don't ask me what the cooldown is because in all the times I've fought him, I've never really kept track of the thing, but my rough guess tends to be at least 20-25 seconds which is more than enough time to burst them from half health.
An early armor item like Zhonya's or at the very least the seeker's part. Should he stack his tornado, either stay far out of range or dodge it, most will not waste it if they can't get a hit off on you so usually will use it to farm. Make sure you're always in tower range if he manages to get an ult off on you, be ready with any CC you have to keep him there.
With any other snowball champ, if he doesn't manage to beat you in lane, he'll try to roam for kills, be aware of that. It only takes one kill or even an assist to get it rolling. In team fights, he should always be the first one taken down. If he's allowed to ult, more than 2 of your teammates, you should be trying to either catch him out or positioning better.