Yep, this is my first ever guide, for one of my favorite champions for both 3v3 and 5v5. Orianna's different play style allows for you to easily control the flow of almost any battle from a reasonably safe distance with the help of her loyal "Pet".

While my guide may seem noobish, before giving any harsh comments I urge you to try it out in a solo top for 3v3 or a mid for 5v5, and maybe you will be left with some good comments afterwards.

Well, these runes are pretty simple, built for the early game boost which will hopefully lead to one or two quick kills via your trusty ball. The runes just give some base ap and mana so that you can do more damage and blast off just one extra ability into the fight.

Again, this is fairly simple, just gives you more ability power, magic penetration, tiny bit of cooldown and some magic resist and armor. This is based solely on getting as much damage as possible out of your spells both early and late game.

Ahh, the dreaded items. I may get shouted at for suggesting some of these items, maybe not, but I have found them useful and relativley easy to get quickly if done in the right order.
Now, the first item I always get is the amplifying tome, because it adds nicely to your early game ap, and also builds into a useful late game item for both you and your team. I also buy a mana potion just so you dont run out at a crucial point in the fight. My second item is yet another amplifying tome, which should be followed shortly if not immediatley by the hextech revolver for some nice tasty spell vamp. this gives orianna surprising survivability while you save up for your first blasting wand then Will of the Ancients. This is a truly amasing item in my opinion, as it not only grants you 80 ability power and 20% spell vamp, but gives your nearby allies 30 ap and 20% spell vamp. This item is great for orianna because whenever she needs health, all she needs to do is send her ball through a wave of minions and back.
The next item you will save up for will be the Archangel's staff, and you should probably get the Tear of the Godess first so you can get some mana regen as well as start to build up it's stack early. After that just get another blasting wand and finish your staff. This is obviously a useful item for Orianna because it provides ALOT of mana, good mana regen and nice ap which will continue to grow as you level up and get more mana. Since you should be playing this build in 3v3 top or 5v5 mid, you should be able to farm minions to get these items fairly quickly. At this point you should be around level 7-9 and have around 160 ap, not bad right? now you can start pushing your lane a bit then moving in to another lane for an easy gank, which I will continue on in the skills section.
The next item, now that you do a good amount of damage(having probably finished or almost finished getting your q to level 5) you will want to get your void staff fast so you can keep doing this damage. Most people I play against will have by now realized the kind of damage Orianna will do, and will be just starting to get some magic resist. Getting the void staff early means you will do more damage to those who havent got MR yet, you will easily cut through those who HAVE bought MR items, and you will deter your opponents from buying more MR, as they know you will cut through roughly half of it( including your masteries). Basically, you will keep doing high damage and theres not much they can do to stop it.
From this point onwards it should be a fairly simple matter to get the remaining items. I prefer to get the Rod of Ages at this point just because by now your opponents will be doing a fairly high amount of damage, and even a few rouge spells might take you out. The Rod deals with this problem, as well as giving you even more ap and mana(which leads to even more ap due to your archangel's staff). Now that you have a good amount of mana, and alot of ap, you should be able to comfortably blast off you ball in ever which direction. This brings me to the king of ap boosting, the Rabadon's Deathcap. with a 140 ap boost AND THEN taking 30% of your total ap and adding it in, you will be effectivley taking out quarters of your enemy's life bar at a time, and slowing them so that your whole team can move in for the kill. Isn't Orianna great?
The final item I usually buy for Orianna is the Lich Bane, it adds 80 more ap( as if you needed it) and allows your autoattack after an ability to deal your ap in magic damage. which means you should be hitting them for a 500 from you ability followed by a 500 auto attack, then everything else you can throw at them. Rinse and repeat.
Some people will be angry with me for not including some 20% cooldown reduction in my item build, but the fact is, after taking your q,w and an auto attack, the other team will be running the other way anyways, and if not, you have the rest of your team flailing away at them with, admittedly much less style than you, but hopefully also doing damage. If an extra second or so of cooldown is really messing your game up that badly,by all means get rid of the Lich Bane, but I will never speak to you again, not that I would speak to you anyways... but still.

Fairly basic, won't spend alot of time on this.
you should be maxing your q as soon as possiblem as it always uses just 59 mana, and does some decent damage if you get it ranked quickly. the second to max should be your w, as your second damage dealer as well as an escape/ chase tool, it is increadibly usefull, but much more costly than your q. last to rank is your e, the shield. at low level it is not great to be honest... and if you max it first you would not do enough damage to have any reason to go into a battle in the first place and thus no use for a shield. As usual grab your ultimate whenever it lets you, in a large team fight it can do good damage, as well as dragging all of your opponents right into your w which should be following, and shortly after that you should see some pretty pictures and letters saying you have killed 3-5 people.
Early game you should really use your q sparingly as you dont have a huge mana pool, once you get some mana you can blast spells as freely as you wish( try to hitn your opponents though). use your w later in the game along with your q as a high damage poke and slow. also use it to speed up one of your team members who needs to escape from a battle, which will also slow anyone chasing him. your e as a shield can be used fairly nicely late game, after you have 500 or so ability power it is not amazing, but usable. I mostly use it just to get the ball to allies so that I can speed them up or follow up with my Ultimate to drag enemies towards our tank. Your ultimate requires careful use, as it is a confusing shot to make if you dont know exactly where your ball is at the time and which way it is in relation to your opponents in order to get the desired pulling effect. Tricky to master. I expect it mastered in 3 minutes readysetgo!

The above information is all I will include for now, as i can;t be bothered to type any more, even though I have quite a bit more to say on the subject... Maybe later if nobody decides that I suck at making these and should probably quit League and play something like Monopoly. You never know.