Orianna needs a lot of AP to do dmg that's why we max out AP items. She uses her ball to attack the enemy and that's need a lot of AP to do dmg. Follow this guide and you will do great dmg in the end.

Runes, I want some AP and cooldown, and the magic penetration.

I use the normal "AP build" 9 0 21

I start out with a dorans ring and purchase Mejai's soulstealer as next item. After that i buy shoes and Rylai's Crystal scepter for some ap and hp. Then i aim for Rabadon's Deathcap. I finish my buy list with Archangel staff (selling dorans ring) and Lich Bane. Alot of AP to orianna so she can do some great dmg.

I start max Command: attack, this skill goes thru the target and when the ball hit the target it do dmg. After that i max out Command: Dissonance this u will combo with Command: attack. And it will get you good dmg. I put in ulti when you can put in ulti. Command: protect i put 1 in lvl 4 becouse it help you and your teammates with the shield u get but i max it last.

Summoner spells I use clarity and flash. Clarity becouse u get oom very easy with orianna and flash to runaway from battles. If I'm going mid i use teleport and clarity.

Follow this guide and you will do a lot of dmg in the end. Play safe and use your skills correct and you will pwn some noobs. I promise this AP build is going to make you do a lot of dmg if your mejai's get stacked. I wrote this guide fast becouse i wanted to tell you about the items and skill masteries and etc. Good Luck!