Take care when running from an enemy with Playful as you can get stuck in some places like the corners of the enemy teams base entrances or even your own.
If in a teamfight you get focused try to use your Chum the Waters and your Urchin Strike when you're at low health and then a quick escape with Playful to deceive the enemy team making them think they can kill you to get an easy kill for your team.
Seastone Trident can deal significant damage early game, allowing Fizz to come out on top of most duels.
Unlike most assassins, Fizz's abilities lacks sustainable means of farming, as maxing Playful to farm will waste a lot of his mana pool and his escape potential. Because of this, it is recommended to max Seastone Trident to max his basic attack damage output and last hit minions under the tower.
It should be noted, however, that the Liandry's Torment's effect will not apply by simply autoattacking with Seastone Trident's passive like most on-hit effects components. It will, however, apply when Fizz uses Urchin Strike, as it apply both on-hit and on-ability effect. In this case, consider building Frozen Mallet on Fizz instead of Rylai's Crystal Scepter, as it not only provides a stronger slow, but more durability for Fizz as well.
Malady is a useful item that increases ability power and attack speed; it also provides an on-hit effect that reduces magic resist with autoattacks, making all your abilities deal more damage.
It is worth noting, however, that a Fizz who plays "hit-and-run," as most do, will get only minimal utility from its MR-shred.
Nashor's Tooth is a decent item, since the active on Seastone Trident deals damage scaling on attack speed; the ability power, cooldown reduction and attack speed all benefit him.
Consider building gold-generating items like Kage's Lucky Pick as Fizz's skillset lacks effective and sustainable means of farming and allows Fizz more opportunity to roam around to gank other lanes. This item can eventually be built into Twin Shadows which gives more magic defense and ability power for Fizz as well as some movement speed to help chase enemies down.
Should Fizz take Heal as one of his Summoner's Spells, consider building Philosopher's Stone instead so he can stay in the lane much longer. This item can later be upgraded to Eleisa's Miracle to lower the cooldown of Heal (be sure to upgrade the item before or on level 15).
Ohmwrecker is a better item for Fizz thanks to his good tower diving ability from Playful and the additional health and AP needed for his build.
An AD Bruiser-ish build also works well on him due to the fact his W deals % damage. The fact that a Bruiser also builds resistances and health (alongside AD) will allow him to stay in team fights as it counters his natural squishiness. It will also compliment his hit-and-run playstyle, as well as any jungling build.
Fizz is fairly squishy early game, and can be easily zoned.
Save your high-damaging spells for when his Playful is on cooldown.
Avoiding his Chum the Waters is extremely important, as it has high AoE damage and a knockup.
Take note that even if you avoid the skillshot, the fish will remain at the end of its path and attach to any champion who walks into its circle.
Remember to activate healing abilities only after his Seastone Trident debuff expires.
Fizz mainly deals magic damage, either through his auto-attacks or his spells. Therefore, investing in magic resistance will mitigate his damage.
Fizz is an incredibly effective counter against casters who utilize skillshots as their primary bursting capacity or initiations. Therefore, avoid picking such champions, a number of which include Kassadin, Anivia, and Zyra.