If you want to beat Zed, first rule is DO NOT let him farm, harrass him as much as you can while farming at the same time.
Also, you must dodge as many Q shots as you can.
The reason people tend to max E first on Zed is because they can't throw skill shots effectively.
But wait until you face a Zed that is actually good at skill shotting, those are the annoying ones.
If you feel squishy against Zed, try getting a gank and also building a bit of tankiness (armor + health).
That will make it harder for Zed to actually push you back. Also, take into consideration that Zed needs high AD in order to execute his damage with efficiency, which means that he will be fairly squishy.
Try to avoid getting hit by double E or Q, that sometimes can be the difference between surviving a full attack by Zed or a gank.