Hi, I'm Nickielikesrice and this is my first guide ever. Some of my friends made some so i thought, might as well give it a shot. :D
Fizz is a super fun to play champ imo. He has a dash that can be used both offensively and defensively ( is that even a word?), a passive/active W that does heaps of damage, and his ult MAKES A SHARK COME OUT OF THE GROUND.

I start with either a dorans ring or boots and three health pots.
Starting with Dorans ring gives me alot more early game power while starting with boots is just like skipping some early game power to go straight into more powerful items.
Then I upgrade my boots into sorcerers shoes for the magic pen. (<3)
From there i build a Rod of Ages and a Rylai's crystal scepter to increase my survivability(if you havent noticed, Fizz is squishy).
Then I build Rabadons deathcapOR Lich Bane. If i build Lich bane first, i follow up with Rabadons and vice versa. There is no "better" if the two, it's just personal preference.
I then finish with any AP item, personally i take Zhonyas for the armour boost, but its up to you.

Im sorta unfamiliar to the new masteries so im not sure about my current setup, but i've tried to make it so that Fizz has survivability early on. While being able to capitalize on his strong early-Mid game.

I take
Ghost
Ignite

I like these spells the most. Even though Fizz's passive is a built in ghost, the movement speed is what we are aiming for. Ignite is used to add more damage to Fizz's very large bag of tricks.

Other good options include:
Exhaust-lets you catch up to those pesky boots buyers.
Surge.-(no icon from mobafire yet.)-Powerful spell THAT WAS MADE FOR FIZZ. :D <3

Nimble fighter {Passive}- This is basically Ghost but with no move speed. He also takes reduced damage from basic attacks which is what makes him a viable jungler along with his W.
URCHIN STRIKE {Q}- This is his Poking/Harrassment skill. Its burst damage is massive early/mid game and is very viable late game to setup a good kill. Also if your closer to your target you'll pass through them so your actually BEHIND them while still doing damage so they cant get away :D
SEASTONE TRIDENT {W}- This is what makes fizz so powerful. IT DOES A PERCENTAGE OF THEIR MISSING HEALTH AS DAMAGE OVER TIME.I MEAN HOW AWESOME IS THAT? any low health champs chasing after you can have the tables quickly turned on them one v one.
Playful/Trickster {E}- This is the skill that gets Fizz out and in and EVERYWHERE. he can jump walls with it, giving him a more or less free flash. But when activated, you hop onto your trident thingy,AND CANT GET TARGETED. So goodbye to Yi or Tryndamere hitting you instantly for a bazillion crit and dying instantly. He can then reactivate it to get away. Boy i love this skill.<3
Chum the waters {R}- This Ultimate is a signature move, i swear it should be made into a meme. He fires a fish that laches onto people, A FISH. :DDD
It then CAUSES A MASSIVE SHARK WHO NEEDS A DENTIST TO BURST OUT OF THE GROUND knocking up (haha) enemies and dealing s=damage. :D Low cooldown for a great ult and it has 3 cc's in one, A SLOE, A KNOCK UP (again, haha) and A KNOCK BACK. Wow. GG.

I think Fizz has a very Hit and Run playstyle, instead of more of a Xin Zhao (running in and petakilling a whole team solo). I aim for the squishies first, preferably the carries and BURST THEM TO HELL.His E works wonders against the carries, as he can just hop away from danger while the rest of your team wipes them off the face of summoners rift.

During the early game, try to zone out your enemy by getting him Low with you Q, and W. Hell, who knows you might even kill the fool. :O

In conclusion, I think that Fizz is SUPER FUN TO PLAY. The fact that hes cute and that i have all his skins helps too. (RP *****) Anyways, i hoped my guide helped out a little, please leave comments below. CONSTRUCTIVE CRITICISM ONLY PLOX. :D

Add me on LoL too: NickieLikesRice.

See you on the fields of Justice :3