When in doubt, play defensively. Let the minions push to under your turret and just sit there (Turret inside of Flash range is usually a good way to stay alive), don't engage at low HP since he'll do bonus damage with his Q. Focus on last hitting and throwing in the odd nuke as harass, take him when you know you can kill him quickly. Stuns are good, slows are okay. Remember that he has no ranged attacks so if you have some space between you and him, then he won't be able to touch you (his W has some range but not enough to be a threat if playing smart).
For instance, if I'm Annie, I'm going to let him push the minion wave and use my Q to last hit. Every now and then I'll throw a Q his way, but more to keep him low. As soon as I hit 6 (I'll have Q, W, E, W, W, R), I'll build up my stun to 3 ranks, then Flash/R onto him, Q, W. If I have ignite then I'll throw that on to, but I like Flash/TP for spells, makes life easier knowing you can recall/TP to get HP back if you're in trouble and your tower won't suffer.
As a bonus, if your lane is pushed towards you, their jungler is going to have a harder time ganking and your jungler will find it easier. That and Ward, Ward, Ward. Just having two wards on the map (bushes outside of Dragon and Baron) can give you a basic idea as to where everyone is. If Fizz has left his lane but hasn't gone past the wards, then he's either at Blue or in the bushes waiting for you. If he's gone past one, then dropping a ping on him should alert your teammates to his presence (having called mia initially of course, this just updates everyone as to where he is) and allows you to push your lane hard and get in a few hits on his tower before pulling back to yours.
Play safe, it helps