Fizz, is an assassin, melee, fighter, with skills that are counted as ranged and an annoying awesome ulti if you know how to use it well. In this guide, i will teach you how to be fizztastic.
-This guide will also show u:
Skill Combos
How to escape
Why i chose what i chose
How to play Fizz on Twisted Treelines
How to gank

Pros
High burst damage
Looks like a fish+toad hybrid
Holds a trident
Can jump over walls with his 'e'
his ulti is a shark
versatile playing style

Cons
Squishy early game
Kind of dead if you get gang banged
Dead when runs out of mana
Can be hard to kill tanks

Top 5 Choices (not in order)
-Flash
-Teleport
-Heal
-Ignite
-Exhaust

You may wonder; why do you choose flash? the reason for this is if u are in early game, and ur almost dead, ull need this spell, along with when ur escaping in early-mid game.

Why teleport? to teleport. durrrhh... so u can get to places faster.

Heal is used for early squishyness, and sometimes, heal is just what u need to beat the other champ

Ignite? One of the best spells ever. Reduces heal, and if u can no longer chase the champion but he/she is almost dead, just pop the ignite.

Exhaust is to slow them down, allowing you to chase them. although i personally think ignite is better.

In both Summoner's Rift + Twisted Treelines-

Early game: Harass, lure, kill.
Q, W, E (x2 if u need), ignite if not dead.

Mid Game: Harass, battle, kill.
Q, W, E(x2), R, Q

Late Game: Fizz on them.
Q, W, R, GG. :D

Core Items:
Doran's Ring-Sustain in Early Game
Sorcerer's Shoes-Magic Penetration, Speed.
Lich Bane-Mana, AP
Nashor's Tooth-Attack Speed, CDR

The rest are just for more ap, mana, regen, etc. If you feel like you are dying too much, you can get rod of ages, or rylais crystal scepter

In both Summoner's Rift and Twisted Treelines, you'll want to go top lane, solo if u can. He needs the farming due to his squishyness and level up quickly. The problem is, it's hard to solo in summoner's rift, so it's good to have a tank/heavy dps/support to lane with. Once you feel like you can gank, u can start going to the bushes, and when you can, use the dash, wound, and if ur dying, start jumping away. :) In twisted treelines, you just walk to the bottom and gank them preferably from behind.

How do you know if you are gonna be good at Fizz?
First of all, here are the characters that I find similar to Fizz:
Talon
Lee Sin
Master Yi
Jax
Katarina

These are all characters that have a jump/dash skill, and/or rely heavily on burst damage, without the use of stealth. They have a similar style of playing, and if you like at least one of them, you'll probably like Fizz. :)