Hello, welcome to my first guide on mobafire!
Because this is my first guide I plan to make it short and to the point. I wont be covering masteries or runes in this guide, as I feel they are all rather self explanatory.
The current meta involves having an AP caster (aka mage) take the mid lane, and Fizz just so happens to be an excellent anti-mage when built and played correctly. I would strongly suggest that you become familiar with Fizz before trying to apply this build/play-stile to him.
Your goal early game is to play aggressively and poke your opponent. ALLOT. Do this using your W to get in, your Q to poke and your E to get out. However, this uses a large amount of manna, so make sure you make it worth your while by getting plenty of auto attacks in-between ability casts. Just remember, you have lots of magic resist on your side, and those pots will give you an advantage too (especially if your opponent starts with Dorans Ring). If its not necessaries, don't use your E. Save it for avoiding ganks or skill shots. You know if you are successful early game if their AP carry has low farm and is behind in levels. After you have destroyed your opponents tower, look for gank opportunities in other lanes. Now you can really start to snowball.

Remember, in team fights your role is to enitiate with your R, take out the most valuable target (usually AP or AD carry), and get out before their body can hit the ground. Your CDR can help you get your spells up quickly so you can jump back into the fight and take on another target.

Please remember that Fizz's W inhibits healing. This works in perfect synergy with Ignite. If there is an enemy with allot of life steal, dive in, ignite and W them. This will pretty much prevent them re-gaining any health and make them allot easier to take down.

If you have pushed to the enemy turret, it is easy to dive enemies. Simply Q in, damage with W and when you E out, the turret will stop targeting you. If you do this correctly, you can get away with taking 1 or even no turret hits.

Fizz's R can be used as an escape mechanism. If you end up in a situation where you are being chased by 2 or more enemies, throw an R at them. If they are clumped together they will all be slowed, and making your escape will be easy. Fizz's R is on a short cool-down (even before you have any CDR), so there is no reason to use it sparingly.

Pros:
very bursty assassin with plenty of magic resist, If he snowballs you can take out half their team before they even know what has hit them. He has extremely high mobility and plenty of escape mechanisms. (He is also a complete pub-stomper)

Cons:
Fizz is very mana dependant early-game, and relies heavily on gold throughout the whole game(who doesn't though). If he's caught with his cool-downs up, or he's silenced, there is pretty much nothing you can do