This is my way to play Fizz. I'm main jungle and I have fun to try some new ways to jungle. In my opinion Fizz is a good pick for the Jungle. So give it a try.
Hope you enjoy the fish in the woods and win some games :) .

Start at Grump and move then to the Blue Buff. Now you can choose if you do the Wolves or move immediately to your Red Buff. If you still have enough HP you can look for a gank or do the Kruggs. Than go back and purchase your first items.

Core Items:

Stalker's Blade - Pink Upgrade:

This Item is very important for Fizz because you stack your attack damage. You need this for your Q because
it does the same DMG as your attack damage.

BotRK:

You get DMG and attack speed. You also get lifesteal and a good active item ability. That's perfect for your playstyle as Fizz.

Sheen / Trinity:

This Item is very good for your build. The passive of Sheen gives you the doubled DMG for basic attacks after spelling an ability. This means that your Q that does the normal DMG and added to that your basic attack DMG does all in all together 200 % DMG of your basic attack DMG. If you have Trinity this effect gives you the tripled DMG. That means 300% of your basic attack DMG. And don't forget the normal Q-DMG.
Also Trinity gives you some attack speed, DMG .... I would say: You get Tons of DMG :D .

Q-Spell: Very good in combination with Trinity. There is more in the chapter Items.

W-Spell: Very good extra DMG per attack.

E-Spell: Invulnerability, DMG ...

Ultimate: After the 5.21 Patch, your ult gives you 20 % more DMG while your target is hit by your fish. This makes your DMG insane!

Fizz is still kind of OP if you play him AD. With this tips I gave you, you should dominate nearly every game. If you have fun and you are successfully give this Guide a like so other people also enjoy this.

Good Luck and Have Fun in the Summoner's Rift!