Why pick Fizz?
Here are some Pros and Cons for this build:

Pros

* Burst
* Easy to chase escaping enemies
* Dodges and escapes ( Karthus)
* Strong early game and late game (if properly fed)
* Crazy snowballing
* Damage over-time!
* Amphibian! (Well, sort of) *Actually, according to Riot, he is "an ancient water-dwelling species." Huh.

Cons

* Squishy (comparable to Annie)
* Need early farm and sustainable gold mid-game
* Hard to be involved in team fights if Chum the Waters is on cool down
* Heavily item-dependent
* Difficult to master
* Many KS with over-time damage => Report and cry

Last games:)

Urchin Strike

Dash a set distance towards or through target dealing significant burst damage. This spell has several uses. When target draws near use it to escape or stay out of range. This can be followed by Playful/Trickster as a basic combo. Used as a gap closer to land a few auto attacks and harrass or sse to dash to minions or jungle creeps to escape.

Seastone Trident

Fizz passively gets auto attacks that 'rend' people - a DoT based on missing health. Active gives auto attacks bonus magic damage. Perfect mage spell because it does not need AD or ArPen to help it scale. Perfect assassin spell because helps you burst down low health targets even more easily. I use it a lot in lane for cheap easy harass.

Playful/Trickster

Fizz can use his trident as a pole-vault making him untargetable while in the air then slowing nearby enemies as the slams back down. If you double tap E he does a double jump and goes further but loses his slow. Hardest skill to master but also the most useful. Use it in a lane to dodge harass then counter with your own. This serves as your main burst. It is also great for chasing and escaping but remember - it only works on small walls.

Chum the Waters

Throws a fish that sticks to its target and slows them. A shark will then come eat the fish and knock up any nearby enemies dealing damage as well. This spell means certain death to anyone it hits in a teamfight. Also use it to follow up on your Urchin and Trickster combo to CC/burst your opponent till your other spells come off cooldown. Take your time and make sure to land it and dont use it to run away.

to be continued...