If you want to be the best mid-carry you can, go Hybrid Orianna. Going hybrid will guarantee you the highest damage output possible with Orianna, and will use the hell out of her passive. It may take a little getting used to if you've been playing her AP for a while, but it'll be rewarding in the end.
For my runes, I start out with flat AP and Magic Penetration, just for that start-game advantage. As with anyone, the better your start, the better your overall.
I simply grab the offense tree, plus the summoner's utility mastery for the CDR on Flash.
With your items, you want to start with your boots and a few pots.
so i've removed this whole section and rewrote it after some experimenting. Changed the build order up a lot. I know start with hextech gunblade, for the active. Saves your life from ganks and gets you so many kills. I then get beserk greaves and lich bane, which gives you a lot higher damage output early game. I then go rabadon's third, like before, and finish it off with BT/nashor's tooth in no particular order. Depends on the situation.
End stats are about 600 ap, around 200 ad, 30% lifesteal, 20% spell vamp, and basics that hit around 1k damage in between abilities (which you can time inbetween each basic, especially with nashor's). about 250 of that 1k dmg will be magic damage, and the rest will be ad, from lich bane's passive. 30% lifesteal on constant 750 basics, plus 20% spellvamp on spammed abilities at 600 ap? i think yes.
[Oh, and blue buff is your best friend; but i'm sure you know that if you're already an Orianna player]
Max out your E first, then Q, for that damage output. 'Nough said.
SURGE. So beautiful for Hybrid Orianna. And Flash is always amazing. I really don't feel the need for ignite, but as with everything, experiment yourself - don't just follow this guide to the point, unless it works perfectly for you.
I'll include all the basic strategy-work in bullet form. I shouldn't really need to say any of this, but a reminder's always nice:
-Farm passively (and a LOT), only last hit and try to keep the farm closer to your turret to avoid ganks from the enemy jungler.
-Poke without being poked (Orianna's great at this), don't be too aggressive, only go in for the kill when you're sure of yourself.
-In team fights, never be the first one in. You ARE a carry, after all.
-Make sure you time your abilities to allow basic attacks in between them.
-Always help your teammates escape death or catch up to their kills with your E and W. Orianna has amazing support skills, and they allow you to attack from an allied champion to ensure kills if needed.
Last note: Orianna's an AMAZING champion, and incredibly versatile; but she doesn't have the highest difficulty in the game for no reason. None of her abilities are massively overpowered or guaranteed hits. You've got to be accurate, quick, and smart. But this is what makes her one of the most fun champions in the game, in my opinion. It IS a strategy game, after all. Screw "________ to win" champions.
Good luck, I hope you enjoy your new Orianna <3