Zed has a very hard time farming and stepping up during laning phase since he only has Shuriken to farm with. Poking him constantly will burn his Health Potions and cause him to be severely behind.
Constantly try push the lane in to his tower and look for roams since he will be most likely standing under tower farming and will not be able to match your roam instantly.
1 kill to the Zed can quickly snowball into many. Invest in armor early to reduce his damage output.
In champion select, grab a Stopwatch and some Biscuit Deliveries! It will significantly make your laning stronger against him since you have more sustain.
Rushing a Zhonya's especially if you're a very squishy champion is ideal. His damage early game is still rather high so getting armor against him right away lowers the ability of getting one-shot dramatically.
When Zed’s is going to finish you off, there is a slight but noticeable shuriken towards your head. Refrain from using your Zhonyas or Hourglass until this signal appears as you might still die if used incorrectly.
Zed's level 3 power spike is very strong. Be careful of him trying to combo you since it can get you very low or even kill you right away. However, if he misses his abilities turn on him instantly since he has no escape.
Zed's level 6 grants him access to his which is extremely useful if a champion has no armor; since ULTing a person and hitting all abilities will always mostly confirm a kill unless they use Stopwatch or Summoner Spells.
Zed is really strong once he has completed one lethality item. During this time you will need to play cautiously and not mindlessly push the wave as he will be able to all in you. Keep the wave somewhat even and do not over extend.