AP conservative
Choose a lane to play. I prefer top solo, and ganks from our jungle when possible.
So basically, you're objective during this phase, is to just last hit. If you can poke when you can, that'll be good; but DO NOT over extend. At level six, since you've out sustained your lane, you should be ahead in levels. At this point it should be a good idea to call jungle or consult with your lane partner to focus and take out one guy. Initiate with your E and then activate your w for more damage, and applying on some regular attacks. IF they flash/ghost/run away be sure to use your q. In most cases you might want to activate your q early (In order to get into they escape path, while landing auto attacks). Remember, try not to initiate all alone, and make sure your partner is ready to jump in. Many a times have I died due to not conversing with my partner. Remember, if you have ignite use it early, as it deals more damage. More damage = less HP = More damage with your W. see how that works?
Play conservative, that's how you shine.

At this point, you should realize the core items are
Rod of ages, Rylai's, and rabadons

After you obtain those three items, there are a couple of questions you ask yourself
IF you spam your skills too much, you want to buy an elesia's miracle.
IF they're getting magic res. You might want to get atma's for the damage you'll have because of your hp.
Banshees is always good, if you need it, becuase they have sorcs, just get that and you should be good.

AD Conservative
Last hit until 6, poke when you can, or call your jungle if he's at 5 and you're at 6. Fizz is really squishy, but has a decent amount of health later on. What you want to do is rush a sheen asap, q to activate sheen/ rush in front of them, and auto attack them as you're doing so. I would Activate Surge after the first hit, and try to keep applying your on hit effects with that awesome W you have. Remember to focus the damage dealers. Not the tanks. I mean you'll do a lot of damage to the tanks regardless, but you want to take in less damage.

As the game goes on you might want to invest in some tank items such as warmogs
But other than that you should be good.