Fizz is a very powerful champion, especially in mid-late game.

EARLY GAME
Stay in lane and farm a ton in early game. Don't be too aggressive or too passive. You want to have loads of gold and be higher level than anyone else.
If they are aggressive grab some extra health pots and put more into your E.
When they attack you in lane, dodge their highest damage dealing with your E, activate your W and if they run chase them down with your Q.

MID-LATE GAME
Push out your lane, but be cautious for ganks. If any enemies are in lane, pushed past half-way, gank them. You can initiate with your Q, W straight away and E when necessary, typically I ult when they are running away. Be careful you are not baited as Fizz does not have much health and this build is not very defensive: this means you can be quite squishie. If you are in a fight you cannot win use your E to jump over thinner walls in the jungle.

SUMMARY
If you follow this guide you should be able to carry your team, getting loads of kills and having fun.

PROS
-Very high damage
-Fun

CONS
-Quite low health