Be sure that your farm is consistent, and you dodge your lane opponents skill shots. Once they are OOM, your life will be extremely easy, so long as you do not use your W to farm so as to keep it as an escape mechanism for unexpected ganks. Unless you are absolutely sure you will win a skirmish, do not fight. This will allow you to scale into mid/late game where Zed hits his power spike. When in lane after Cutlass has been purchased, be sure to fast push your mid lane and farm the side camps to maximize gold income. Keep the deaths low and the farm high, and you're all set to win some Freelo!!

When Team Fighting, be sure to wait until the major CCs of the enemy team have been used, then find the enemy carries (preferably the ADC because the enemy APC will probably have Zhonya's Hourglass by now) and demolish them. A good trick is to throw Zed's W outside of a teamfight, ult in and combo someone, then re-activate the W and wait for an opportunity to rejoin the fight. Although that strategy seems like you are leaving your team to die, it is very confusing and frustrating for the enemy team when Zed jumps in and out of fights uncontrollably!