This guide is intended to be an introduction to the lovely automaton Orianna and her companion, the Evil Metal Ball of Doom. This guide will be broken down into a Quick Play guide (say, for those that decided to play her and are trying to learn how on the loading screen) and then a longer guide consisting of explanations of the Masteries and Runes, Summoner Spells and Abilities, Build (Item) Order, Strategy, Tactics, and Tips, and finally, an area to show calculations (since Mobafire doesn't like to account for things like the 3% from Archangel's Staff.

Why do I love Orianna? Besides the fact she sounds very similar to one of the cute little turrets from Portal? How about controlling a slightly- disturbing giant mass of metal and destroying your enemies with that, all the while frolicking like a ballerina? How about being able to carry, support, and 1v2 in many instances, and do so decently all with the same build? How about that wonderful ult, capable of flinging escaping enemies back into your allies, while dealing a nice chunk of damage at the same time, and then immediately hitting your w to slow them all down? Did I mention the ball gives a passive AR and MR resistance to whatever ally it's attached to? And that you can cause them to gain a temporary shield at the same time with it? Read on, if any of this interests you. :D

Summoner Spells:

If you're a generally aggressive player (meaning with Orianna you'll get closer than you ought), pick Ignite and Flash.
If you're doubtful, like to hang back more, or don't trust yourself to control your mana, pick Clarity and Flash. If you hate her slow speed, replace one of those with Teleport.

Abilities:

Max Command: Attack first, as it is the most versatile and useful of your abilities, and does good damage per mana to boot. Max Command: Dissonance next, as it's your AoE damage/slow/haste all in one. Max Command: Protect last, as while technically the most cost-effective, it's challenging to use (especially without experience) effectively, and the shield rarely saves you or an ally, even maxed. Obviously, Max Command: Shockwave when you can.

Strategy:

Early on, Orianna is rather squishy, and she has a very low base speed. This build will fix the speed enough, and if you keep your distance, you'll deal quite well with the squishiness. Learn the distance of your attacks, and your leash range quickly, because you'll be using both to their limits constantly. Orianna can do any lane well enough, don't worry. However, if you aren't mid, lane with an Assassin/Melee DPS as your spike damage and slow/ult works very well with them. Mana may be a problem so don't use your abilities on minion waves unless an enemy is next to them. Your job in team fights is to beat them senseless with a metal ball, group them together, and pull them back into the fight. Your favorite combo in team fights will be Q->R->W. Use Q to get close to a set of enemies, R to throw them all into one spot, and W to slow them all so your team can eat them alive. This combo is both simple and potent if done at the right time.

The Mastery build is a pretty basic 9/0/21 build. The points between Expanded Mind , Meditation , and Good Hands can float around a bit without much effect, I've noticed. Not much else to say, really.

I'll admit, I suck with runes. My rune suggestion is probably not the best, and gives nada in anything like durability or mana control. I realize I'm suggesting not to get a chalice AND not get MP5 runes, but honestly, with a single potion I can usually make it to the 7 or 8 minute mark before I'm OOM, and I usually need to go get my items then, anyway. Feel entirely free to suggest other runes (preferably with an explanation why they're better), and if it makes sense, I'll probably list them as an alternative if not as the main set. Right now it seems pretty clear: increase your damage through straight AP and MPen. If you look at the calculations below, that 14.22 MPen is absolutely delicious. Most champs start at around 30 MR, and you over halve that between your runes and your Archaic Knowledge . I'm personally a fan, but I repeat, I suck with runes.

Recommended Spells:

Flash Teleport Clarity

Yes, there are three I would recommend. The reason for this is threefold: Orianna has no true escape/closing the distance method, so Flash is wonderful. With her low speed and no abilities to really boost it, flash can make all the difference. Teleport uses this reasoning as well: long distances in short amounts of time, simply. Clarity, I personally don't use, but I strongly recommend it for anyone who spams abilities too much-- If I try, I can run out even in endgame, so it has it's uses. Just be sure to move a point over to improving it's effect for your allies' benefits, yeah?

Optional:

Clairvoyance Orianna is often played as an off-support, and this is a basic support spell. Immensely useful, but you can actually bush-check with Command: Attack both from the sound of the hit and from the sight your sphere gives, so I leave it to a true support.
Exhaust This is an excellent choice if you notice many enemies just barely getting away-- you know, if you notice they're getting away while still within the 550 range of the spell. I'd pick this everyday if the range was extended, but the better question is, why am I that close with Orianna to begin with?
Ghost I like the utility in Ghost because it helps you get back to lane faster, run away from ganks, and chase runners, but a raw percentage of her speed is not that impressive when her speed is unimpressive to begin with.
Cleanse I love Cleanse, too, but think about it: if you're getting hard CC'd to the point you need to Cleanse, is there really much of a chance of escape anyway, given that you're Orianna?
IgniteFirstly, if you don't play very aggressively, Ignite may not be a good choice, and what further, it's max range is 600, significantly smaller than Command: Attack's range, so you have to put yourself needlessly in danger to use it. I can see it being used in cases where a melee DPS is wailing on you, but I rather save a spot for Flash and Ghost to use in unison if you're really worried about that situation.

Please Don't Use These:

Heal Not a support, and has the range to not get hit very much, so why?
Rally Should anyone use this, ever?
Fortify Orianna is occasionally a support in some ways, this is just not a very good way to choose.
Revive I have seen this used to awesome effect with across-the-map revenge kills. You have none of that capability.
Smite Jungrianna? I think not. Even if that's kind of a nice portmanteau.

Abilities:

Command: Attack This is your most important ability. Without knowing from where, when, and how to position your ball, everything else won't work. I can't recommend Smart Casting enough for this exact reason.
Command: Dissonance This is an AoE that also drops a 3-second duration area of increased ally speed and decreased enemy speed. It's what you'll follow up Attack with to harass, strategically drop to help gank/avoid ganks, as well as what you'll drop after your ult to push the team fight in your favor even more.
Command: Protect While hurting every enemy in its path, this is your shield ability that can target you or your ally. Not only does it provide a somewhat decent shield, but having the ball on an ally passively increases their AR and MR (at 18) by 30. That's pretty nice, right? Your tanks thing so, too. As does just about anyone else.
Command: Shockwave Ah, Orianna's ult. With an increased range compared to Dissonance, this simultaneously throws and hurts the enemy. This can disrupt channeled effects, pull back running enemies, and generally confuse everyone effected by it. Your allies love you for this spell, especially a Nunu & Willump/ Fiddlesticks/ Katarina that wants to use their ult. Here's a fun fact: it throws all enemies an equal amount, meaning those near the edges will move toward the center, and those near the center will move toward the edge.

Early Game:

So first of all, you should get B1HP1MP. I personally find that since I can keep distance so well between her abilities and the Boots, I don't need the extra health pot, and since Orianna is so mana-hungry early game, the mana pot is totally worth it, and with the 50g extra, get a second if you're worried. This is also why the next item you're getting is the Tear of the Goddess. Honestly, if you want to build a Meki Pendant first and then get the Tear and Boots on your first time back, that works, too. I don't unless I'm very certain I won't need the speed, since running away is basically the only strategy Orianna has for escaping early ganks/bushhuggers.

Mid Game:

After your early success, the general build goes Will of the Ancients and Fiendish Codex, which is another set of items you can switch up if you want. Now you may notice that this is not a support build, yet I have WotA on here. Why? Spell Vamp! It only applies 33% of your Spell vamp to each attack, since virtually everything you're going to do is AoE, but there are plenty of minions around...this is a great way to improve your sustainability, and the percentage means it will stay useful all game. Combine that with your -20MR from Abyssal Mask and 20 Magic Penetration, and look at all that health you'll be getting! Fiendish Codex is fun to get early on because of the CDR, though if you wanted you could get Archangel's Staff first if you happen to have enough gold by the time you get to the shop. Either way, get the WotA because spell vamp is sexy, especially if you team with an assassin (e.g. Orianna/ Akali team is awesome burst damage after you get WotA). Just for reference, assuming you hit a wave of 3 fighter, 3 caster minions with Command: Attack at 18 with your spell vamp, that's ~226 health gained right there from your spell vamp, which equates to 12.5% of your total health. Tasty? I think so.

Late Game:

After you already have at least Tear of the Goddess, Sorcerer's Shoes, Will of the Ancients, and Fiendish Codex, it is usually a good idea to make that Tear into an Archangel's Staff. Who doesn't love an instant, substantial boost to both MP5 and AP? From there you upgrade to your Morello's Evil Tome for even better CDR, MP5, and AP. After that you start building your survivability items, in whichever order is most pertinent-- fed Tristana? Get Zhonya's Hourglass first, but a fed Annie? Definitely go with the Abyssal Mask.

Replacement items:

Depending on the enemy composition, you may want to switch out one or more items to better suit your needs. AD-heavy team, ganky, or lots of CC? You may get rid of the Abyssal Mask for a Frozen Heart or Banshee's Veil. AP-heavy team, lots of spike damage? Get rid of the Zhonya's Hourglass for a Force of Nature or a Guardian Angel, depending on what you judge is the best.

Note about Lich Bane:
Many Orianna builds get Lich Bane, for both its great stats and unique passive. With Lich Bane, Orianna has the potential to do an even larger amount of damage all the way around, and move faster to boot. However, the problem with this is that she only has a 500 autoattack range, meaning you have to get 300 range closer than normal to be able to reap the passive's ability. I'm not saying it's a bad item, but the entire idea behind Orianna is that the ball does all the work while you're safely sitting at a distance, prepared to get a head start running if need be, due to your overall slow speed. Autoattack Orianna just doesn't work with this build at all, and I haven't actually seen one that has worked very well with a different build, either. I'd leave it to another character, personally.

Note about Tear of the Goddess
I foresee many people criticizing my choice of using Tear. To which I retort, why? Orianna needs MP5 and a large amount of mana never hurts, and it later builds into her Archangel's Staff. Getting a Philosopher's Stone or Chalice of Harmony also give her MP5 and in some ways are better early on, but that money is a waste, when Tear builds directly into one of the more expensive items on this build.

Why I chose my items:
Making this build has been a lot of trial and error on my part. I have done many matches with many different combinations of items-- for a long time I was sure that Rabadon's Deathcap, Rylai's Crystal Scepter, and Void Staff were essential parts of her build; this only changed when my team was doing especially poorly one match, and I forewent Rabadon's and Void Staff for the last two items in my build, Abyssal Mask and Zhonya's Hourglass. The survivability improvement was incredible, and my damage was only slightly decreased. Afterward I switched them out and eventually found the setup you see now. I've always done pretty well with Orianna, but this particular item setup is the most consistently useful and effective I've used with her. I don't doubt the success with other builds-- I've used many-- but this one has a nice amount of lane sustain, survivability, and power. If you can think of a better item build, tell me about it and hopefully show some evidence that it's better, and I'll be glad to change this guide-- I only know that I like this build and it works out well, by no means do I believe this is necessarily the best. :)

Your AP does not cap out at 443.74. It maxes at 560.74 with Archangel's Staff.
AAS Calc: 443.74+(443.74*.03)=560.74 AP

Theoretical Damage Per Ability at 18, Assuming 0MR:
Q: Command: Attack220+(.6*AP) = 220+(.6*560.74) = 220+336.44 = 556.444 Theoretical Damage on first target
W: Command: Dissonance250+(.6*560.74) = 250+336.44 = 586.444 Theoretical Damage
E: Command: Protect180+(.45*560.74) = 180+252.333 = 432.333 Theoretical Damage
and 240+(.4*560.74) = 240+224.296 = 464.296 Theoretical Shield Strength
R: Command: Shockwave300+(.7*560.74) = 300+392.518 = 692.518 Theoretical Damage

Damage and Spell Vamp Output Examples at 18, including 80MR:
Enemy has 80MR:
80-20(from AS)=60MR
60-20(MPen from boots)=40MR
40-14.22(MPen from Runes) = 25.78MR
25.78*.85(15%MPen from Archaic Knowledge mastery) = 21.91MR
21.91MR =17.97% Damage Reduction, or 82.03% damage received
Q: Command: Attack556.444*.8203= 456.451 Damage Dealt and 456.451*.25*.33 = 37.657 Spell Vamp from first target
W: Command: Dissonance586.444*.8203 = 481.06 Damage Dealt and 481.06*.25*.33 = 39.687 Spell Vamp per target
E: Command: Protect432.333*.8203 = 354.643 Damage Dealt and 354.643*.25*.33 = 29.258 Spell Vamp per target
R: Command: Shockwave692.518*.8203 = 568.073 Damage Dealt and 568.073*.25*.33 = 46.866 Spell Vamp per target

Damage Per Mana Cost, Single Target
Q: Command: Attack 456.451/60 = 7.608 Damage/Mana
W: Command: Dissonance 481.06/110 = 4.373 Damage/Mana
E: Command: Protect 354.643/40 = 8.866 Damage/Mana
R: Command: Shockwave 568.073/150 = 3.787 Damage/Mana