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 Banshee's Veil 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's attacks becomes more deadly for a few seconds after he uses his empowered attack - keep him away while his trident is glowing!
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!