Welcome to my guide, I am an OTP Orianna Support player that plays almost exclusively SoloQ games. I don't play the game often enough but I am currently ranked Diamond 1 (playing only Orianna Support) and the highest I reached playing her was Master.

Orianna is an enchanter support that excels in mid to late game. Her most important abilities are her shield which also gives extra defense, her speed control from her W, and her ultimate ability which can be a gamechanger if use well, but can be very unreliable when use from your ally. Orianna's biggest advanate over other enchanter supports' is her range, and that enables her to support melee allies from a safe distance. Cooldown reduction is the most important statistic on her, followed by shield power and ability power.

Moonstone is the first item to rush, you build it first in all games, it's one of your power spikes. After first recall you would ideally want to build mana regeneration item for 900 gold, but if you recalled early buy mana regeneration for sure.
Next you need boots, about this time is a good time to roam for her, or it might be late already, that's why I take free boots from inspiration tree.

Next you build Flowing water, ALWAYS START BUILDING ITEMS FROM THEIR MANA REGENERATION SIDE, you will have issues with mana until late game.

Next is Redemption - good stats, and great passive ability, redemption + your shield-ultimate combo is the greatest combo you will have enitre game. Yeah, let's just double the survivability of your ally, and deal some meaningful damage to your enemies in one go - a game changer.

And Dawn Core at last. There are no alternative here, it's just too good to pass.

The only thing you could change in this order is buying Redemption before Flowing Water, or buying Censer instead of Flowing water. It's possible these might be better in some cases than original, detailed decription in next chapter.

Upgrade you support item into Dream Maker.

Just an explaination why this items and this order of building them.

I have an AD champion that I support not AP, why not Ardent Censer instead of Flowing Water?
The answer is very simple, where is cooldown reduction? I don't need your extra speed Mister Censer, give me my cooldown reduction. I'd rather buy Flowing Water because it will give ME a few nice bonuses instead of this Censer which only my supported ally benefits from. I get extra cooldown reduction, extra ability power from the Flowing Water. Censer gives me nothing. And the extra ability power given to my allies? Even if they are AD focused, most champions benefits even a little from extra AP. It still might be a good item for 5% percent of the games but it's such a niche use case and since you don't know who you will be supporting in the game I just discarded it as a possibility.

Helia?
Orianna doesn't have time to focus on damage dealing, you spend all the time spamming your W on your allies and casting your shield when necessary

Mikael?
I never tried it. But it doesn't look very good anyways, if you want swap it for your redemption or maybe flowing water, but you will have problems to use it since Orianna is all about range, and you will be out of range to use it when you need it.

Aery is a must, there are no alternatives. In battles poor aery doesn't even have a second to rest since your low cooldowns' and Aery's ability to proc from previously casted W make it run back and forth all the time.

Why not Scorch?
It can be very usefull early when you have the right adc, but they are rare and you have your issues with mana early game. It's better to go for extra ability power since you'll sit passively most of the time until level 6.

Secondary runes are just my personal preference, I like free boots because I have to rush moonstone anyway and it let's me roam just at the moment when I need it.
Jack of all trades is just a little extra cooldown and AP, but you usually get it very early - after your first recall, you can go with summoner spell's cooldown also. Other viable otpions are Resolve runes (especially Revitalize), and at least on paper cooldown reduction from precision looks the best, but they come really late.

Until level 6 you usually don't have a lot to say, just cast shields on your ally and use your AA (remember your passive). You just have to wait it out and not die too much). At level 1-2 though you can harass your enemies but it's not always viable, with a good ally it's possible to crush your enemies before level 6 although it's very rare.
At level 6 you have your first tool to initiate a fight but it's not reliable and not always possible. You often want your ally to initiate the fight not you, but it depends. I often see and easy double kill, just please Ashe shoot your ultimate at their ADC, that's all I need to give us the double but what I often see is arrow flying towards my top, well maybe it's the time to leave this lane as I won't be able to achieve anything there and start roaming.

It depends on the game but you usually want to start roaming around level 6 or after moonstone is built. But how to make a decision? It's simple. Are you able to achieve anything by stayng bot lane? Maybe some kills, maybe hittting tower? If not just go assist your jungler/mid, mostly jungler.

And you better hope that your jungler is not a terrible player because that's usually your partner. But what about ADC? I should support them. - Nope. If your ADC is really good player then you might stay with them all the time but middle game usually means supporting jungler. Follow them all the time, help them with ganks, help them clear camps faster, speed him up with your W, and take the blue buff if possible, and alongside all of that provide vision. Orianna is often a 2v5 champion so if you play well and have good jungler you can snowball this playstyle and crush the enemy.

But if your jungler is bad then it might be better to stay with ADC, or go assist your middle/top, provide vision, you usually want to stick with the strongest player in your team and assist him all the time. Finding the best player can be tricky though, and if you have issues with choosing that player, sticking to jungler is usually the best bet.

Especially when you are going into late game, you were assisting jungler, but the game is still not decided, gold is plenty, builds'are full or close to full, it's not really necessary to help your jungler anymore, especially if he is starting to fall behind, he might not picked to late game ultimate killer champion. You might want to change your supported ally, maybe there is a good late-game ADC player (Vayne) at the bottom, but you lost your lane 0-4 because you both have late-game focused champions. Maybe your mid or top are overperforming. You can change your supported ally if it benefits your chances to win. But don't change them too often.

The only choice is at level 3 when you can level up your E or W.
I usually go with E, main reason being you don't really have mana to cast W.
But W can be escpecially usefull to hinder enemy melee support from initiating.