Orianna is by far one of the most fun characters I have ever played in LoL. Not only does she excel at harass, but she has one of the best scouting abilities in the game. If people play her correctly, she can quickly become an absolutely beastly carry.

Pretty self-explanatory. I chose the mana regen over ap for the seals because early on in the game you really want to be able to take advantage of orianna's harass. In other words, don't be shy about using your q and w if you think you can get a hit on them. In any case, you'll be running out of mana pretty quickly and will want the early regen. Coupled with doran's ring, you should be fine in the lane without having to go back for mana.

Also pretty self-explanatory. I chose the ionian boots over magic pen. because the CD reduction is crucial for Orianna. She can toss out some amazing damage from just her q and w combo alone. Spamming this for harassment as well as teamfights is essential, which is why I welcome the CD reduction.

Rod of ages in general is just an all around great item for ap, mana based characters. I sometimes prolong getting the ionian boots if I wish to rush the rod. I chose to get the catalyst converter over the blasting wand first because the health+mana you gain from leveling really helps you stay in the lane for longer periods at that level.

Rylai's scepter is just such a useful item. It's great for increasing orianna's survivability and the slow helps both, escape from enemies with your w (or help your allies escape) and hunting fleeing champions down.

Archangel's staff was also included before Rabadon's due to the need to increase your burst damage. Orianna has the ability to deal out terrifying amounts of aoe damage, which is why I prioritize the AP over mana.

Once you sell off the doran's ring, the void staff is a pretty nice item to complete your set. At this point, Orianna should have over 3k health, over 5k mana, 450+ AP, and be a little terrifying. The void staff is the best magic penetration item you can get, and, if you've been playing orianna right, the other team should have some magic resist at this point.

This is up for some debate. I prioritize harassment and dealing damage to enemies, which is why I ignore Orianna's e until I have to get it, at which point it becomes very useful. By the time I get it, it usually blocks a significant amount of dmg and I can spam it all I want. However, early on I have found it difficult to find it as useful as upgrading the q and w. If you are midding as well, you especially want to upgrade your q and w first to apply serious pressure to your lane.

For team fights, you DO NOT want to be running into the foray immediately. Because all of Orianna's abilities center around her ball, you need to hang back for a second or two after the engagement has begun and pick out what point you want to throw your ball at.

Some tips for where to target:

Be aware of who's likely to be targeted first. Usually teams will immediately go for the carry (hopefully that will be you, but you'll be hanging back so that won't happen) or a feeder. In any case, watch for them to run up to that champion and act accordingly.

Look for their carries. Orianna's ult is great for disrupting a team fight and can keep a carry out of a battle for a second while you and your team dish out the damage.

Target the squishies. I don't know why, but for some reason I notice that squishy character like to stay close to each other during teamfights. It may just be me, but in any case, if you see it, feel free to immediately throw the ball at them and hit w and r. Orianna has such great burst damage that they should be at at least half health by that time.

Other tips:

Orianna's ball is godly for scouting. I cannot say how many times I have been saved by first sending my ball into a bush to check around and finding 3+ champions waiting for my mechanical butt. It has relatively low mana cost as you level up, so feel free to spam it for scouting. I have even stolen Baron with it once by sending it from the above cliff and ulting.

Well that's pretty much it. This is a work in progress, and I did it all at 5 in the morning. So... feel free to leave any suggestions you might have and thanks for reading.