Welcome to my Orianna Build.
Change Log:
June 02: Released
June 06: Changes in the build
History of Orianna:
There once was a Piltovian man named Corin Reveck who had a daughter named Orianna, whom he loved more than anything else in the world. Though Orianna had incredible talent for dancing, she was deeply fascinated by the champions of the League of Legends. This fascination compelled her to begin training to become such a champion. It is unfortunate that her sheltered, wide-eyed naivete led her to take unnecessary and dangerous chances which ultimately led to her tragic demise. Orianna's death shattered Corin, driving him into deep depression and an obsession with techmaturgy. He could not stand the void his daughter's death left in his life, so he decided to build a replacement – one that would complete Orianna's dream of joining the League. What was created is the clockwork killing machine that Corin named after his daughter. Knowing that she was destined to be a champion and seeing the way the times were changing, he created The Ball as her pet and protector. This nearly symbiotic creation uses a different type of techmaturgy, relying more heavily on electricity than clockwork.
Orianna and The Ball now fight as Champions in the League of Legends, using the Clockwork Girl's sometimes misguided morality as a compass. She tries in earnest to fit in with those around her. However, no matter how hard she tries, Orianna can never be human and there is always something unnerving and alien about her. Though she attempts social interaction with other champions in the League of Legends, there are few who can get past her exotic nature. To many, it's as if there's nothing inside, that Orianna is just a soulless clockwork shell – a dangerous and deadly one at that. However, all along she remains the perfect daughter in her father's eyes.

"Dance with me, my pet. Dance with me into oblivion."

Well, I bought the Orianna double bundle the day it came out, and I haven't stopped playing her (with this build) yet. And, in the future, I will be adding more builds to this, as more ways to play her develop, i.e. support etc.
Hope you like it!

Greater Mark of Insight-Magic Pen. Needed. Obviously.
Greater Seal of Clarity-You can't to wrong with mana regen.
Greater Glyph of Potency-AP Baby!
Greater Quint of Intellect-Mana. Just flat mana. Good for early game.
Greater Quint of Replenishment-It gives some mana regen early game, you need it.

Offense-9: Some AP stuff, magic pen.
Defense-0
Utility-21: Mana regen, stuff for her summoner spells, Exp Gain, all that.

Starting Off:
Mana Crystal, 2 Health Potions. Orianna is mana STARVED early game, if you're playing her right. So, get a Mana Crystal. Then just grab 2 health pots. Orianna seems VERY easy to damage early game, so they'll come in handy.
Next:
Ionian Boots of Lucidity, Catalyst the Protector. You can buy these in whatever order works better for you. Ionian Boots because Orianna needs jut a LITTLE bit of CDR. Catalyst is a must, and you'll build it into your Rod of Ages. Besides, the passive works well with Orianna, as well as many other champs.
Next:
Rod of Ages, Rylai's Crystal Scepter. Rod of Ages, is the item I prefer as a boost from your Catalyst. Rylai's has the slow passive, necessary, and enough health to remove Orianna from the squishy zone.
Next:
Rabadon's Deathcap, Zhonya's Hourglass. Orianna's source of AP. That simple.
Lastly:
Lich Bane. Orianna is rather slow, and this gives her just a bit of Mov. Speed. to boost her up a bit. The passive works well with your innate, too. You can't go wrong with a little bit more AP and Mana, either. Then, to top it off, just a little bit of Magic Resist.
Optional Switches
Archangel's Staff:
Archangel's Staff can be switched with Rod of Ages, depending on your playstyle and your need of mana from spamming.

Command: Attack- Always max this first. It will be your major source of damage throughout the game.
Command: Dissonance- I like this to max second, but it depends on how you play, your team, and the enemy team. Can be switched order-wise with Command: Protect.
Command: Protect- Your shield. I prefer to max it last, but you can max it second if the team you're playing against is just whomping on you.
Command: Shockwave- It is your ult. Fill in the blank.

Summoner Spells:
Flash- Good for quick escapes and catch-ups, works well with Orianna range.
Ghost- Chases. What I would pick second, but can be swapped out.
Teleport- Gets you places quicker. Can be swapped with Ghost.
Clarity- Restores mana. Is good early game, but unnecessary late game.

Well, that would be all. Remember, I will be adding more builds to this as Orianna progresses and such. Thanks for reading!