Masteries go 21-9, Damage quints and Armor pen marks.
Things to be aware of with abilities:
Q: This is a large source of your damage so make sure to land these, be aware it only does full damage to first target hit (including creeps) and 60% to all targets after. Also be aware that it only deals 50% damage for every extra shuriken that lands on a target. By no means does this mean you should only worry about landing one, you can land a max of three shurikens (one from zed himself, one from w shadows, and one from ult shadow), if all land that's a 200% damage increase from only one landing and makes a big difference.
W: Pretty straight forward, can be used as an escape or gap close or to extend your poke in lane, does not interrupt movement or actions. High cooldown though so be aware of possible ganks and positioning in teamfights.
E: Damages and slows all targets around you, damage does not stack from multiple E's overlapping but the slow DOES. Every champion hit from E whether by zed himself or his shadows cuts 2 seconds off your w cooldown timer. Highest you can get is -10 seconds off your w if on cooldown by hitting all 5 enemy champions with your E. Also E can be cast while AAing without cancelling your AA unlike your Q which is important to know!
R: This is your burst damage and can also be used to make fancy escapes (yes I said escapes) and plays if you're cool enough and wear fancy sunglasses. Keep in mind where you start your ult is where your return shadow will be so initiate with your ult accordingly, also a shuriken will appear above the enemy champions head if you've done enough damage to kill them when your mark pops. You will always appear behind the person you ult, also zed's ult is extremely predictable which is part of the reason his teamfighting is lackluster in the late game if not horribly fed. Be aware of enemy CC when ulting into a team in a fight as a good support or anyone with cc for that matter will look to lock you down or peel you off that squishy carry you're trying to blow up which can really ruin your day. Also be aware if the person you're ulting has zhonyas or QSS as either of these items are a hard counter to your ult and can also ruin your day. Cleanse WILL NOT remove your mark.
As Zed a lot of your strength comes from your laning power, roaming and split pushing. Don't think your only job is to blow up their carry and that's it. Typically your Combo's want to go something along the lines of R - AAE - W - Q - AA - E - AA/out, if you land your q's that second auto attack should be procing your passive and once you're done with the combo it should be enough damage for the mark to finish them in most cases. When placing your W after an ult use it to stick to the person you're trying to blow up, be aware of escape they have and where they're most likely to use it and place your W accordingly. Also once you shadow back to your ults original shadow you'll leave a shadow behind, the ults shadow lasts much longer than your W and typically will last long enough to get a second Q off, this can be extremely helpful if the enemy you tried blowing up just barely made it with a sliver of health as you can catch a lot of people off guard with a Shadow shuriken right before it disappears.
I'm only Gold but I've played a lot of Zed, I hope this help :)