Some info on me:
I'm a summoner level 30 dude who plays on EU West, my summoner name is ExtremKB and this is my first build on MobaFire so be nice!

Since this is a very basci guide no fancy numbers and calculations will be included. Just a straight outline of how I play Fizz and how you should play him as well.

Fizz is as you know a meele AP kind of bursty assasin. I picked him up the first day he was released after seeing his spotlight because he looked kind of unique, and he is.
With Fizz you can pull of some cool tricks, be very mobile and smack your enemies across their face with your trident for huge amounts of damage.
I tried Fizz with a lot of different builds but I came up with this one after playing a game that went on forever. I decided to pick up Lich Bane an right away I noticed the difference.
Lich Bane + Fizz] = LEGENDARY

Pros:

He's very mobile (Two gap closers wuuut)
Has great damage (with this build)
Easy farm with

Seastone Trident and Playful / Trickster
Hes good the whole game, early to end.
It's one of few, if not first water element Champion in the game
Sharks, yes Sharks. Not gay Dolphins, but SHARKS


Cons(BUUU):

He's squishy, no **** okay we got it almost all AP casters are squishy duhh.
No CC, well two tiny slows and a little "push"
Might take some time getting used to playing
He is melee. Not necessarily a CON but some might say
If you don't like fish, this champion is not for you... sailors and fishermen will enjoy grandmaster fizz

So yeah not much to say here really. With the new masteries system i advice you to go 21-0-9 and not 9-0-21 like you probably used to.
With your runes setup and these masteries you get a nice early game damage. But beware you will be squishy!

Very basic, magic penetration is always a friend, the reason i pick armor is because it goes so well with his passive. Thay annoying early game Caitlin or Xin will have a hard time knocking you around wit their basic attacks! The rest is self explanatory, The quints give you 15 AP to start with, and even better if you choose to start with Amplifying Tome you will have some decent AP for a level 1 champion!

I know i wrote Ghost and Ignite
But I replace Ghost with Flash
Since Fizz already is very mobile and has a dash as well as his playful/trickster flash isn't always necessary.

OTHER VIABLE CHOICES

Flash
Exhaust

I want to explain my item build and why it is so great.
As you already know Lich Bane is freaking great on Fizz.
When you activate Seastone Trident and then do use your Playful / Trickster you will do HUGE amounts of damage. It's insane how you will be able to nuke down minion waves, wraiths, wolves, multiple champions in a teamfight you name it. I strongly recommend Lich Bane

Most of my other item choices are pretty common in other builds as well except for ONE
Nashor's Tooth

You guys : ARE YOU INSANE??
Me: Poker Face

My friends Nashors tooth is probably the greatest invention ever for Fizz
The attack speed and cooldown reduction and mana regen RAWR it's just great. Everything goes so well with Fizz!
Attack speed + Seastone Triden will be Fizz's best friend.... except for water, water is probably his best friend... and sharks.

Other items:
Void Staff very nice item, gives some MP which is useful if the enemy bastards are going MR.
Rod of Ages Personally I don't really like this item and I don't use it, but if you feel like you need it... then whatever ... I don't like you.
[[Mejaias Soulstealer}} always nice if you are doing good and stacking them kills up.
Morello's Evil Tome Veeery nice item actually! Why? CD reduction and AP and all that dude.

Defensive items:
quicksilver sah always good! Replace Banshes with it if you want to. Situational
Guardian Angel Some nice defensive stats, and that annoying revive. I recommend you useing only one of the three defensive items that I have stated so replace this with Banshee's Veil

Before I end this guide/build I want to add this.
This guide is far from finished an there's lots of room for improvement I know. But before you judge it, please try it. If you don't like it then tell me.
Criticism is a great way for me to know what I could have done better and what I should change.
Here are two games with this build the others are off my match history unfortunately.
If you do good with this build , feel free sharing it with me and the others.