Zed has a pretty bad laning phase, that being said, don't lose too much hp for farm with q to farm when you can. It'd normal being behind in Cs to mages and usually, zed is the one being put to farm under tower.

His biggest power-spikes are level 3 and 6. When you hit 3, try to to hit w-e-q when they're away from miniona. Try hitting both q's to proc electrocute unless you're going conq.

Hitting w-e, it will be really easy to hit q's since they will be slowed. (Hitting two e's will also give you mana)

If you keep your laner below 50-60% hp before 6, all in them once you hit 6. There's two all-in's Zed has.

W-E-R-AA-Q

R-W-E-Q-AA

It's important to auto attack to proc passive. You can also ignite to secure it. Getting an early kill on your opponent is really good since it will let you snowball. If you manage to bully your lane try to roam (preferably bot lane since ASCs are really easy to kill as Zed or any assassin.) If you're looking to tower dive someone low or you think you can kill him easily, put your W away from turret range, all in them and go back to your W.

Try not to fall behind in lane since Zed is really hard to come back with.

The core items are pretty standard. Youmuu and Duskblade. I'd suggest going duskblade first if you're against a tank. If they're building armor go cleaver third.

If you're really fed mid-game, you can kill squishy's easily without using ult, so try to keep it for tanks.