Passive
His Passive is like Phantomdancer and its good when u run behind a enemy through a minions wave or things like this.
Q
Q is the spells which Fizz uses to make dmg cause it is very good with LICH BANE cause then u make the dmg of Q + Ur AD + 75% of ur normal AP!
W
W is good to farm and its like ignite and u can use it to reduce the heals of the enemies
E
E is a good ability to come out of fights or go in and with E u cant get amed by spells or attacks from enemies.
R
Ur Ult is the spell which makes the most dmg in teamfights. It is the best to throw ur ult on the enemie ADC cause it good to focus him then cause he cant come away.

The Counters of Fizz are:
-Ryze
-Garen
-Teemo
Counter Items:
-Zhonyas
-Guardian Angel
-Magic Resist

Fizz counters the following Champions:
-Katarina
-Mundo
-Karthus
-Ahri
-Sion (AD)
-Nunu
-Ashe
-Cho Gath
-Soraka
-Sona
-Nida (AP)
-Morde

WIth Fizz its important to use zonyas cause whith it u get out of the focus and when u use E and Guardian Angel u get out of the focus for more then 5 sec but before u use Zhonyas first throw ur ult and then active Zhonyas and w8 for the dmg of ur ult.

LICH BANE is good for the Q and its the most important item for Fizz. With this item and Fizz' Q u can steal every kill.

LAST HITTING IS VERY IMPORTANT and it is very easy with his W.

Fizz cant help much in Teamfights but he can gank easy in early game.

Very important is that u take ignite, flash isnt so important cause Fizz can jump out with his E so or so but ignite is very good with his W.

Important is that u spell Q first and then W cause with this Combo u make the most DMG.

The herase combo is:
W+Q+E Away or R+W+Q+E Away
For Teamfights:
R+W+Q+E then Zhonyas then W+Q and Flash away or too the last enemy
When enemies herase u:
E w8 then again E away