I'm mostly on the mage side of the matchup, but I am more than familiar with playing Zed as well, which is how I come to these conclusions. These do assume equal skill level, that you're not eating bad trades because you have poor knowledge of laning relative to your opponent.
If I am Zed, we both base around level 5 or 6 and you come back with
and some
s , you are going to die very soon unless you have a gimmick like
,
,
, et cetera do. This purchase offers little in the way of firepower, offers no defenses, and the sustain from
does not help you if you get one-shot, because again, you have no defenses.
If I am Zed and you come back with
and
, I am going to have a bad time. Health, armor, and sustain are very strong into Zed. Once you have Rod of Ages and Seeker's Armguard you will have a lot of effective health due having purchased health and armor, you are going to outpush me from a safer distance, be able to take a full combo with my ult and Ignite and live 1v1, and you will have outscaled my "cheese" period of the game.
These are not absolute. Zed can kill someone with
and a mage with
can 1v1 Zed and live. These are recommendations for players who can not effectively match Zed at their current skill level.
Beyond the above, I see too many players playing passively against Zed pre-6 or even after when they should objectively have the upper hand. If Zed uses his W, throw your poke at him and avoid the range of the W shadow so he can't swap to it and hit you. At early levels, his W has a very long cooldown and this is your window to continue to abuse him. Don't allow him to farm for free without getting an autoattack and poke ability onto him whenever his W is down. This will give you a health advantage, especially prior to level 6 so he will be far less likely to all-in you. It will likely give you a CS advantage because he can't play forward if he is at low health.
Zed needs to be able to get ahead to be effective mid-game. If he can't get ahead for mid-game, he is going to have trouble remaining relevant. Zed is out wave-cleared by every mage and many assassins in the game. If he can't match you 1v1, he can't splitpush. If he can't waveclear for his team or splitpush effectively, he has to teamfight. Zed doesn't have the strongest teamfight presence when he has not snowballed, so the likelihood of his success goes down considerably.
If these pointers don't help you succeed against Zed, I would be happy to live coach the matchup with you 1v1.