This is my first guide, so please bear with me on this one. Also, this guide pretty unorthodox, but through testing in normal games, it seems to work fine.
Many people sees Orianna as a support champion, and they would probably be right. However,when I first played Orianna during her time in the Champion Rotation, I saw potential in her passive, thus leading me to typing this guide. I think this build relies more on Carrying the team and relying less on Orianna's skills more than any other Orianna build out there. However, this does not imply that you forget about her skills completely. Orianna's skills are very important in different scenarios. For example, when escaping back to a tower, using "Command: Dissonance" to boost Orianna's and her allies movement speed and slowing her enemies, can be the one key to your survival. Another example is utilizing "Command: Shockwave" as an AoE damage and pull enemies away from an escaping ally or Orianna herself.
In all honesty, I'm typing this guide as sort of a copyright safety net, as I do not wish for other Summoners to take credit for my idea (though I am not completely certain I am the first to have this idea cross their mind(pardon my greed). Please keep in mind this guide is just my personal opinion to my idea. Feel free to derive other builds from this build to suit you, but please: give credit where it is due. :)

Summoner Spells:
For the Summoner Skills, I chose Clarity and Flash.

This build was made to take some stress off of Orianna's mana,so there is no need for mana regen. items. As a substitute, I chose Clarity. Clarity works phenomenally when laning with a mana user, as you have the Clarity Upgrade Mastery. The one important note about this Summoner Skill is to remember to use it. Many times I have watched my enemies get away with 1 or 2 bars of health, and secs later, I've realized Clarity was done cooling-down, waiting for me to abuse my abilities. I would always be disappointed, as I would need the extra gold to continue my build.

As for Flash, it is one of the best Summoner Skills in the game, so why not? Orianna can utilize it when chasing down her ally (this tactic is most potent when combining "Command: Dissonance" or "Command: Shockwave"), or simply just cheating death (again, very potent when using previously mentioned skill.

Runes

Attack Speed Quints: You can replace with almost anything. I personally adore Dodge Quints, but for this build, attack speed seems more appropriate.

Magic Pen. Marks: Orianna's passive gives bonus damage in the form of magic damage, so this works nicely. You can replace with attack speed.

A.P per lvl Glyphs: Orianna's passive gives bonus depending on her A.P so this would help. You can replace with magic resist or armor if you are concerned by her survival. However, the A.P per lvl Glyphs are always a better option than flat glyphs, surpassing it by lvl 6.

This Rune set-up is just my opinion. Changing these for anything that relates to Attack Speed or Ability should work fine in theory.

Masteries

10 in Offense: mostly for the attack speed bonus and A.P
20 in Utility: mostly for the Summoner Skills Upgrades and the Experience Boost.

Switching the masteries around shouldn't ruin the build, so whatever suits you most.

I always start with Dorian's Ring, but Boots of Speed and health potions can work to decrease Recalls. Afterwords, I rush a Beserker's Greaves, to increase harassment and mobility when laning. To increase Orianna's survival chances, I rush a Rylai's Crystal Scepter. The recipe route this the Scepter varies depending on your situation. If your team is getting pushed hard and you start to die once or twice, get the Giant's Belt, followed by either one of the A.P items. Vice-Versa, get the Ability Rod, the book, the belt. After this, I get a Sword of the Divine, as this item seems very ideal. Afterwords, I would try and rush the core of this build; the Rabadon's Deathcap and the Phantom Dancers.

I had mentioned "Command: Dissonance" a couple of times previously in this guide, so it would be apparent to max it out as soon as possible. However, this is not the case. During gameplay,it benefits me more to max out "Command: Attack" early than "Command: Dissonance". Perhaps it is because I am more likely to an enemy using "Command: Attack" than "Command: Dissonance". Whatever the case, I always max out "Command: Attack" first, alternatively leveling up "Command: Dissonance" when it is available. I intend to break the mold of using Orianna as a support champion, so I upgrade "Command: Protect" last. I do this because I expect me and my teammates to not be reckless enough to need my help. Though it may sound selfish, it is completely logical. Orianna's "Command: Dissonance" should be enough to help my ally escape while slowing down the chaser. The other reason why I prefer "Command: Dissonance" over "Command: Protect" as a support skill is because, when I use it on an ally that it fighting a losing fight, it psychologically encourages (however small the scale) them to fight on, thus dying. "Command: Shockwave" is to be leveled whenever it is available, obviously.
During early game or laning phase, it is important to use "Command: Attack" followed by "Command: Dissonance" to harass as much as possible. The cool down on these two skills are relatively short, so Orianna can use it to escape when being harassed.
The rest of the game is up to you to play as well as you can.

Again,this build can be changed to suit you, so feel free to mess around with the build. Please do not steal and thank you for your time :D. Happy hunting!