Since Fizz can move through units, find opportunities in lane to walk through minions and apply Seastone Trident's passive - following it up with the ability's active attack after a few seconds.
Fizz's ultimate ability, Chum the Waters, can be aimed at an enemy or towards the area where you think they'll be going.
Fizz's spells scale off Ability Power - consider getting items like Zhonya's Hourglass or Abyssal Scepter against teams that have high burst threat - and items like Lich Bane or Rabadon's Deathcap if you think you can survive without the Health.
Fizz becomes extremely deadly if his damage over time ability ticks on you for a few seconds - keep him away until it falls off!
Fizz is a slippery target when his abilities are not on cooldown - bait him into using them early and follow up with crowd control or hard-hitting attacks!