Fizz is a powerfull assassin with very high damage and good resistance if is it build right.
Example: http://www.youtube.com/watch?v=kxFbMNKEv5o

Greater Marks-magic pen (normal runes for an ap assassin)
Greater Seals-health regen (fizz is very weak in early game, if you are playing against aggressive players you have to stay on the line at farm how much you can)
Greater Glyph-ap per level(normal runes for ap)
Greater Quitns-flat ap(normal runes for ap)

Ignite-best spell in combination with his passive from w
Flash-That's why I take flash : http://www.youtube.com/watch?v=R4odW_7nMAM

Farm how much you can until lvl 4-5 when you will can start to harras your enemy.
Note:Don't try to engage before that you will remain with no mana and you will have to go base to soon + you are very weak in early game ,so you can dye very easy.
At lvl 6-7 you should have 1,2,3 kills if no you should start to:
-go aggressive agains't your enemy (better no if it's your counter pick)
-catch their jungler at buffs (if the jungler is not feeded)
-ganks top/bot
In late game at teamfights stayback and w8 for their ap/ad carry to come in your range or try killing him from back.
Note:Don't be the first/second only if you are very feeded so you can kill them all.

In early/mid use w for fast creeping.
In late use E to kill massive waves of minions.