Attack Damage Marks help you last hit in lane and trade more efficiently as Zed's abilities all scale well with Attack Damage.
Armor Seals are very standard and help you mitigate some early game auto attack harass and minion damage.
Magic Resist Glyphs are absolutely neccessary vs AP casters and also help mitigate some of Orianna's early game poke with her abilities and her auto attack passive.
Armor Penetration Quints help you do more damage even if the enemy starts cloth armor vs you, provided they do, otherwise it simply lowers their armor further thus amplifying your damage more.
Going 21/9 in masteries is essential for Zed because he is an assassin and thus wants as much damage amplification as he can get whilst taking 9 points in defense to help him lane and make him a bit tankier at the start of the game.
Noteworthy is that a lot of people will put 2 points into butcher albeit Zed's passive utterly negates the need for that as it helps you secure last hits with the bonus magic damage that it does.
The 2 points in sorcery are not neccessary however there is nothing else worth puting them into lest someone wants to take Destruction which is fine too.
Lastly, the bonus resistances that are picked up can be swapped depending on the lane matchup however for the most part, Zed wants the bonus Magic Resist more than he wants the bonus Armor vs Orianna.
The priority of what you want to max is as follows;
Death Mark (R) > Razor Shuriken (Q) > Shadow Slash (E) > Living Shadow (W)
The reason you max your Q is because it allows you to farm effectively from range, poke from a safe distance and also waveclear decently.
Second you will max your E due to the increased damage it will do and its effectivity in clearing waves during the mid game.
Lastly you max your W which will decrease its cooldown and start amplifying your Attack Damage due to its passive.
Whilst maxing in this order you put a point into your ultimate whenever you can.
There are a few items which can be bought initially to help lane vs Orianna.
The most effective item to help lane vs an Orianna up to the level 6 is a Dorans Shield due to its passive and health regen it will help you stay in lane and farm whilst being able to take some damage from her autos and regen over time.
Your level 1 start would look like this:
Starting with these items will mean that your damage will suffer a little due to you not going for something that boosts your offensive stats so it is wise to try and wait for a jungle gank if you want to all in her. However, if you manage to harass Orianna a lot with your WQ Combo or Q alone and she drops low, you can easily pick up a kill on her even with this start.
Your first back should be at around level 6. You want to complete that Bilgewater Cutlass as soon as you can! If you are forced to back earlier you can pick up a Doran's Sword and some more Potions along with a Ward or two.
So depending on how well you managed to farm, you will return to lane with either of these two build paths;
Alternatively to build path two, you might be set a little behind and only get a Vampiric Scepter instead of a Bilgewater Cutlass.
During the first 5 levels it is important that you try and farm as much as you can to get your core items. Often it is better to lasthit ranged creeps with your Q and auto attacking to the melee creeps to last hit them. When you can, you want to poke Orianna with your Q.
NEVER use your shadow to harass if you do not have at least one side of your lane warded or if you have not spotted their jungler somewhere on the map where he can take advantage of your shadow being on cooldown. The reason I say that you need atleast "one" side of your lane warded is so that you can "play on that side". Thus you know you are safe there and if the jungler comes from there, you can leave towards the other side and in turn if the jungler comes from the unwarded side you know you are safe to run to the side you did ward.
If you do see the jungler on a different side of the map you can harass Orianna with your WEQ Combo. Here you can apply the slow from your WE first to make landing your Q easier. When possible, you want to make sure both Q's hit Orianna to deal more damage.
Once you reach level 6 and Orianna has no Zhonya it becomes an easier lane for you than it is for her. Now the threat that you can kill her is larger than previously and you should harass her as much as you can as long as you have vision on their jungler or warded one side of your lane.
The core part of this match up is that you dodge a part of Oriannas combo. Either her ultimate or her QW combo need to be dodged in order for you to survive a 1v1 without dropping so low that you might trade a kill for a kill.
If you have poked her down and feel as though you can kill her with your ultimate, make sure you have full energy and then engage preferably with your ultimate, instantly casting E and Q thereafter.
At this point she will most likely retaliate. Here you need to use your W or your ultimate clone on R to dodge he combo or ult. If you slow her with your Bilgewater Cutlass, you can use your shadow clone to gain some distance from her ball and then re-engage with your ultimate clone. This needs to be done in rapid succession so that your ultimate clone doesnt dissipate while you are far away from her.
If you go even in lane, or all goes well and you get a kill you want to complete your Blade of the Ruined King and can start working your Last Whisper or Brutalizer depending on how much armor the enemy team is buying.
Ideally you want to complete the BotRK and Mercury Treads to help you mitigate some damage and be less subsceptible to slows.
Zed has a few core items and limited build paths, this is the most standard build path:
This buildpath is effective against Orianna. It offers high burst, damage mitigation and sustain whilst also giving Zed some Cooldown Reduction.
The boots choice is dependant on the enemy team and its composition. If there is a lot of Crowd Control on the enemy team, you should buy Mercury Treads. If there is not a lot of Crowd Control on the enemy team you can pick up Ionian Boots of Lucidity to reduce your Ultimate cooldown and help you secure kills by roaming.
There are a few more items I will discuss however;
Frozen Mallet is not a good choice for Zed. He is an assassin and needs to go pure damage to be effecient at what he does in the late game. Granted the slow is nice, but you have your WE to slow and you ideally want to Insta-Gib a squishy late game rather than chase them with auto attacks. Additionally, Zed has enough mobility to keep up with his opponents so he really doesnt need this item.
Tabis are good when the enemy team has multiple Auto Attacking based champions in their line up thus mitigating a large portion of their damage.
Randuins is similary situation to Ninja Tabis, it helps when the enemy team has many Auto Attacking based champions or Attack Damage based champions in general.
Youmous is only good when youre far enough ahead to complete it and want to Insta-Gib enemy carries with your ultimate and the ensuing combo. However it is not good when you are going even or are behind.
(Pro Tip: Due to the nature of armor penetration change in season 3 the way it stacks can cause your midgame to spike insanely if you follow the "Tri-Pen" Build that is standard in high elo Dominion, Brutalizer>Last Whisper> Black Cleaver > Brutalizer > Youmous. Upon catching someone you activate Youmous and ult them, this build does INSANE burst damage but lacks sustain for a very long time thus making laning very hard)
Sword of the Divine is similar to Youmous in the sense that it is great when you are fed, but lackluster when you are behind or going even. Quite simply put, other items simply offer more.
Hydra is nice for clearing waves, but Zed has no problem doing that regardless, the reason that most players build BotRK and not Hydra is because the active from BotRK allows Zed's ultimate to do more damage because it is also considered when the DOT(second portion of Zed's ult) damage triggers. Some might still argue for Hydra over BotRK but the general consensus is that BotRK is simply better due to its active and the synergy with Zed's ult.
Spirit Visage is an interesting Item but not really that effective on Zed, A Guardians Angel and Maw of Malmortius are enough resistance against magic damage as that Zed does not need even more MR.
In late game teamfights Zed wants to ultimate the target that can not stop him from Insta-Gibbing them. Thus you need to watch out if the Orianna in the enemy team has used her Zhonya or doesnt have one at all. In this case you can easily engage on her, use your ultimate and burst her down whilst saving your W to escape.
Sometimes the best course of action vs Orianna is to ultimate her, use your combo and flash away or use your W to make sure she cant land her ultimate on you and then re-engage with the mobility spell you have ready that being what you didnt use to get away from her.