Zed is a highly mobile assassin, which means getting to the back line is typically not too hard and getting picks is easy. It is important to focus ADCs and squishy glass cannon targets so your team can melt down the rest without worrying about the carries. Zed's role in the early game is to use his passive and farm minions, against a ranged caster however use q to avoid taking too much poke. Mid-game is very strong for Zed so use your W-E-Q combo to burst a squishy down for an easy kill. Zed's late game scales well and his role is to get to the back line, and get back out to kite the enemies left. Zed is a very strong champion and in my opinion, once mastered, a very good carry.
Items used when playing zed are normally the same but differentiate against different damage types. Against AP, I recommend an early Hexdrinker and Ghostblade if you are even or ahead in lane. If not, go a full Maw of Malmorus and Merc treads into Ghostblade then follow the rest of the build path discluding either Duskblade or Hydra. Against an AD champion, go Ghostblade or Duskblade 1st and 2nd item. Duskblade is very strong and many people underestimate its damage combined with Zeds ultimate. If you can, get Ninja Tabbies 2nd or 3rd item and disclude Maw of Malmorus.
Zed's primary combo is W-E-Q but alot of people never put the shadow back into action. If your combo does enough damage at level 6, bait the enemy into coming close to it after "fake" backing away then quickly advance to the shadow and all in them if you see a chance. This is a VERY useful technique and has gotten me personally MANY leads leading into wins. Another combo is placing down a W before you R to give you more mobility and playmaking during a duel or assassination.
During a Teamfight, always go for the glass cannon carry, usually the ADC but varies among who is stronger so your team can fight the rest without worrying about the damage. As Zed, it is very important to get picks and his W-E-Q Auto into passive combo is a very good burst at doing so. In a teamfight try to assassinate anyone in backline and burst them to where the deathmark will finish them off, the return to your R shadow. It is very important to get the kill if you can or put in extra damage than the minimum for deathmark to kill as the target may have heal, barrier, etc.
During laning phase, Zed is very good at farming because of his passive. Scale E 2nd against an agro melee champion because trades will work better and so will farming minions with the AOE of Zed's E. If against a ranged caster try to use Q alot to get minions out of range of autos because ranged champions have an advantage and tend to zone melee champions. Mid to Late game split push when objectives aren't being prioritized and maybe get Boots of Mobility to make sure you are back with your team for an objective. Zed has very good AOE clear with his E and Hydra so I recommend getting it.