Start long sword and 3 pots to sustain in lane. Its up to you to decide whether you want to push or not. I prefer to let it shove just before my tower and freeze it there. If you don't know what freezing is go learn it.
In the laning phase keep management on your energy and cooldowns. If you're getting zoned its quite possible to get most of the cs only using his abilities, they are very short cooldown and almost resource less. Only use your shadow to help poke in lane, if you know where the jungler is. Its his only reliable escape and the cooldown is fairly long. If you do decide to poke using your shadow it can help to use e first to slow them to land the shurikens easier. Remember his shuriken does a lot more damage to the first target, so avoid pushing the lane by throwing your shurikens through all the minions. Try to aim it at angles in order to just barely touch him. Zed is a strong laner revolving around constant pressure and poke to whittle down enemies before going in and decimating them, so keep in mind his combo pre 6 will usually not kill the enemy outright, you need to poke them down first.
After you get ult, you have a lot of options. At this point, begin to keep your eye on the map more and your objective in lane should be to poke the enemy laner down low enough to where you know you can kill them.
The most basic combo for zed is to use your ult, throw your shadow forward, e, and then try to land multiple shurikens and ignite them, then shift to your shadow because they will have most likely run forward to it. Auto once to trigger your passive before shifting back to your ultimate shadow and to safety. REMEMBER TO WEAVE AUTOS IN UNLESS ITS TOO DANGEROUS TOO.
In the middle game try to get picks or small fights and keep up the pressure. Roam to help other lanes and stack up items. In teamfights you want to go for the carries but you don't want to get caught by the tanks first, so I usually like to sit off to the side in the fog of war before making a move. In middle game teamfights, you want to use your shadow, then shift to it and ult in quick succession to get to your target quick. Execute your combo and then back out. Wait for your cooldowns and help your teammates when you can.
As for runes and masteries, taking flat ad should be fine, with armor seals, and 10% scaling cd glyphs, and scaling magic resist. Masteries I used to take warlords but since it only now stacks on champs, theres no real point. Thunderlords is just too good, so go 12/18 with whatever ones you like more.
Build order should be similar most games with some exceptions, an early
is always helpful, and perhaps think of
to get even more cooldown.
are all great items on zed. If they're tanky consider getting of the last whisper items. If the enemy is an aggressive mage such as ahri or brand, consider getting a
to ensure some safety in the laning phase.
As late game comes around, its up to you to decide whether team fighting or split pushing is the better option. In any case, make decisions carefully and be sure to at least kill 1 person you mark.