It's a team thing. Generally the support or tank keeps Zed off your ass, since an assassin is supposed to 100-0 the adc and escape. Your team's job is to make that difficult or outright impossible, but you can't do it singlehandedly typically.
You can build
, abuse bush vision tricks to outplay with Vayne or Graves and bursing Zed while he's stunned/blinded, but generally you don't want to interact with him unless he's cc'd. If you got a bruiser on the team, their job is to kick his ass and lock him down (think Darius or Vi, or hell even Garen can do it) so the team can blow him up.
Your job, as the adc, is to provide sustained damage in a teamfight and shred the frontline while yours protects you. Don't try to 1v1 the assassin, the odds are not in your favor.