Okay, I'll go through every phase of the game
Pre-game
Preferably a top lane > jungle tank
Usually take armor seals and normal masteries
Take exhaust if you often lose against him (i personally don't take exhaust, but it is a good idea to deny him 1v1)
Pre-3
This is probably where Zed is weakest and you can really make him suffer the first two levels. AA him every time he even goes near a creep, and if you feel brave, try zoning him all the way to his turret (not pushing, just zoning). Just make sure that you don't get ganked tho.
When Zed hits level 3, he has way more options for damage, as he unlocks his basic combo that synergizes really well with Thunderlord's Decree. I would consider starting to poke him with max range spells (like Viktor E, Azir soldiers, generally spells that have stupid range)
If you're playing something like Vel'Koz or Syndra, you can prepare your all in combos for him. Not for all inning, but to get some damage onto him. He has to farm melee most of the time, and his CS movement is still very predictable.
Level 6
If you're not already ahead, get an Armguard and always play with more than 80% HP. He will be able to do alot of damage if you don't have any defence, so playing without exhaust or summoners is very dangerous.
Avoid following his path when he is roaming, because he might surpise you from a river bush or something (goes for pretty much every champion). It is very important to keep track of him, not only for yourself, but also your bot lane. A 2/0 Zed on bot lane is really unfortunate and he will just start to annihalate you.
Mid-late game
Usually stay grouped as 5 after the laning phase. Traditional mages have way better teamfighting options than Zed. Have a tank, exhaust or something peel so he doesnt get to blast someone. He really starts being useless if he cant pick out someone to kill instant.
Zed as a champion doesn't fall off, but the ways mid and late games are played are just a counter to assassins. Sometimes, and it does happen that Zed gets fed into the mid-late game, simply because teams can't play around him