I hope you like my guide to Fizz. Here is a guide on playing full AP Fizz.

If you do not have ult, W, Q then E onto the enemy. If they aren't dead, basic attack them or ignite them (ignite would help at any point in your combo, especially if they're running away) and when your abilities are back up, use them. If you have R, hit the enemy and perform your combo (W, Q, E) while the shark is about to come up. If you are out of mana, dying, or you screw up or miss ult, you can use your e to get away (unless you can still kill them despite messing up). If our e is on cd, use flash or run until your e is up. You can use your zhonyas to not die if you want.