The standard Zed harass trick is to throw a W down near your opponent, E them, than W for max damage as they run away. What you have to keep in mind whenever you use your W is that you are now without a gap closer, making it really easy for champs like Fizz, Yasuo, Riven, Annie(good ones), etc, to land massive amounts of damage on you. If you are ever in doubt of if you should use your W to harass, it might be a better idea to play defensively and harass with just your Q.
While many zed players rush Bortk, I've found that item isn't as good as people make it out to be in some cases. Don't get me wrong it's a fantastic item in every way, but I tend to rush a last whisper in the majority of match ups. Here's why:
If you start with a longsword than with halfway decent farming you can pick up a pickaxe on your first back, which is a pretty good powerspike comparatively.
When you finish the LW, your death mark damage will be huge. You shred armor in chunks due to the fact no one builds armor early game and if you land your whole combo it will almost always result in a kill. The only champ I haven't 100-0 using his ult has been a Garen running full health and armor runes and masteries. Even if you don't kill them they will have to back which affords you the chance to gain a cs lead.
Keep in mind that rushing a LW is a pretty ballsy/snowbally approach to zed, so you need to roam asap and secure more kills to get your second item(Bortk 99% of the time).
Using death mark effectively depends entirely on you keeping track of which abilities your opponent has on cd.
Let's take a fizz matchup for example (basically because I think zed vs fizz is entirely skill based). Fizz has q,w, flash and ignite and ult but his e is down. Zed has everything while running flash and ignite. The big thing you want to keep in mind is that fizz has 2 gap closers(q, flash), while zed has 3(ult, flash, w) so if you ult fizz he can blow his flash and q to escape. In this case you obviously use your flash and w to keep up with him, and make sure your e, ignite, aa with passive proc, and w if you can hit it is enough to kill him. We're just assuming he doesn't have zhonyas. If so you would need to bait that out somehow and kill him after.
I run standard ad masteries, flat ad runes for more early game kill potential, and a longsword and 3 pots to start. If I know I'll be farming under tower for a while (heim, malz) than I'll start dorans and one pot, and run lifesteal quints (passive synergy is too good).
Finally, try him top lane. He is a viable pick vs common top laners due to the great poke, high damage and low cd he has. I highly recommend him vs Darius in fact. One of the easiest lanes I've ever played.
Im only S1 but I hoped that helped and let me know if you have any questions!
(upgrade to whatever is appropriate that game)
or 
(to combo with your ult, use it after you initiate your ult)
(or 
or 
)
(Pick a defensive item for this slot)