Orianna can be built a few different ways, in this guide I will be building/playing her as more of a harasser, small nuker and all around disabler. She is an amazing support and has some fairly decent damage as well.

Pros:
+Easy harass
+Doesn't have a lot of mana problems after early game
+Gets quite a bit of health with this build
+Doesn't need a lot of ap to do a lot of damage
+Skills scale well with ap
+Very versatile character

Cons:
-Slow(300 ms)
-To play effectively need a decent understanding of game strategy
-Versatility is sometimes a little intimidating for newer players

Clockwork Windup
This passive makes your auto attacks deal extra magic damage based on a percentage of you total ap. It can really help you last hit minions better.

Command: Attack
Sends your ball flying to target location doing damage along the way. This is an excellent harass skill, it doesn't require that much mana and deals surprising decent damage with great ap scaling. Use this skill to set up ball positioning for ganks and slow, behind you and Command: Dissonance for the slow to help your team get away(or just use it while the ball is attached to you to also get the speed boost), to set up your ulti, and more.

Command: Dissonance
A small aoe that does decent damage and leaves an aura that slows and speeds up enemies and allies respectively. Combined with Command: Attack it is a really good harass, also a very good team escape skill and ganking skill.

Command: Protect
An awesome support move! Sends ball to protect yourself or an ally, damages enemies along the path it travels to reach target. Useful for protecting that ally that is leading the charge for the teamfight/gank, great for protecting that ally that is getting focused down, or hit a teemo shroom, even ignite. This skill is so useful, you can use it in many ways to save your teammates. It can also be used offensively by placing on an ally that is near the middle of the fray (where you should never be as a caster!) and then use Command: Dissonance to damage and slow most of the enemies, also good for setting up your ulti!

Command: Shockwave
All around an amazing ulti! Great for helping your team escape by throwing your ball behind you and ulti when they pass it to pull them backwards, great for ganking by throwing infront of them for the damage then ulti for the pull back and then use your w to slow them.

I choose this skill sequence because this gives you a very good early game harass which means you can more or less try to outfarm your lane opponents due to constantly whacking them with your ball.

If you chose a total support role starting early game then I would max out your e first for the protecting it offers.

Flash
This is, in my opinion, one of the best escape spells in the game, just flash over a wall or use in in combination with a bush juke and you are good to go.

Ghost
Since Orianna is so slow this is a very useful skill, especially if you need to run to help and ally or run to a team fight or just anywhere on the map really.

Start out with Doran's Ring it gives some nice starting hp, 15 ap and some mana/5 which all help sustainability and harassment.

On your first trip back if you have enough get Catalyst the Protector if not then just get tier one boots and either a Ruby Shard or a Sapphire Crystal

Build the Catalyst into a Rod of Ages, then look at the enemy team comp and if they have 3 or more people with a stun, slow, or any cc then get Mercury's Treads if not then just get Ionian Boots of Lucidity

From here try to build a Rylai's Crystal Scepter once you have that you should have quite a bit of health and some decent ap and a nice slow that can work for all of your abilities and makes your slow aoe even more effective!

If the game is still going try to build a Rabadon's Deathcap

I put a Will of the Ancients down next, I know some people aren't big fans of this item but it's cheap, 2100g, and gives you 40 ap + an aura that gives you and your allies 30 ap and %25 spell vamp. (note, the 30 ap from the aura stacks with it's base 40 so you get 70 ap!)

After that the game should be over, if not then look and what you really need.
-Are they hitting you with a lot of cc's? Make sure you aren't standing too close or in the middle of the teamfights, if they still hit you then work on a Banshee's Veil
-If you are getting blasted down by enemy casters then get something like an Abyssal Mask
-If their 10-0 yi is moving at 520 and has 2.5 att speed and 300 damage then get a Frozen Heart it gives great armor and a lot of mana
-If you don't need any of these then just buy anything you feel you need at the time.

When a team fight starts try to stay in the back out of harms way but close enough to fire off your skills and still have a presence. When an ally is getting focused or initiating then send your ball to protect them and also line yourself up for your first volley of skills. Whenever you can use your Q to send it through as many champs as possible, but try to make it land in the middle of them to line up your W! Then use your W to do an aoe damage and then use E to protect and ally and also possibly do some damage on the way to him. If they are trying to escape use your Q to send the ball in front of them then use R as soon as they pass in to pull them back and then W to slow them and buff allies, use E as necessary. If your team is trying to escape then do the same thing but behind you!

v1.0.0.120

Orianna

Clockwork Windup
Fixed a display error on the tooltip.
Fixed a bug which was causing Clockwork Windup to add less damage than intended
Fixed a bug with Command: Protect that was causing the shield particle to not display
Fixed several interactions with clones or unusual movement types
(This really doesn't change anything for the playstyle!)

Orianna is a very useful and viable character to have on a team. She has a lot of versatility and potential. She can slow/buff, harass at will, protect self/ally, and pull enemies away/to her.

I don't consider myself an expert on her at all, these are just my notes on what I think about her and I thought I would share it. This is not a failsafe, %100 percent win guide! Just the way that fits my playstyle.

Enjoy! Don't forget to comment when you vote so you can help me improve this guide for the better!