"Zed is an assassin with utility".
Zed has some of the worst utility of any assassin in the entire game, he brings a single moderate strength AoE slow which is predictable in its location (always centered on his shadow) and costs him a gap closer / escape.
That said, someone who said "like you do a bad zed" but better is pretty much correct. Yes, Zed's shurikens hit you over the creeps.. And do 65% of their original damage as a result; I.E. not a huge problem, it's not like Zed is the only champion who has skillshots which go through minions. Zed has a nasty all-in which bursts hard and lets him escape quickly. Also true, but so do champions like Ahri and Leblance, where as someone like Swain has an all-in which laughs off your damage and Malzahar just locks you in place while he 70% - 0%'s you. Mid laners tend to have ways to kill enemy laners when things go their way, who'd have thunk it?
The biggest things that you need to work on with Zed are pretty simple.
1:** Be aware of where his fucking shadow is.** Plenty of players will see Zed back off after unloading his shadow.. And then step forwards. Giving him an easy shuriken target / letting him get a slice off, or even letting him port next to them and start unloading auto attacks.
2:** Be aware of his shadow cooldown.** This is pretty standard stuff, have an idea of your enemy laner's cooldowns and count them. When his shadow is down, that's the time to zone him and get aggressive; it removes a lot of his options and you'll find it surprisingly easy to punish Zed for blowing it. Zed's shadow has a 4 second duration and an 18 second cooldown, so until level 13 or so it will have roughly a 22.5% uptime in lane - as in it will exist for that much of the lane if he uses it on cooldown every time. Play around that and capitalize on weakness, but shy away from strength.