My guide for Quinn, Demacias newest carry.

Why I chose these items

There are other ways to build her, some of which may turn out to be more successful, but this is what I personally have had fairly good games using. I like to get the boots and health potions in the beginning for the help in running or chasing, using vault to either get in range and slow, while causing a large amount of damage, or when they stun me for their jungler to gank me, if they are not cautious and get infront of me, i can vault backwards towards my tower while slowing the biggest threat to me at the time.

While some people would prefer to go into a bloodthirster early on for decent damage and give themselves lifesteal early. I prefer to go for the movement speed, attack speed, and critical chance, because when you mix this into the character, her passive is multiplicative with her overall attack speed, instead of multiplying the base and adding on top, giving her a much higher attack speed than most.
Going into a static shiv after making the bilgewater, will give her critical chance, attack speed, an on-hit damage procc which added in with poking using her vault, can cause serious harm, and still lifesteal due to the bilgewater. Afterwards, finishing up the boots and getting the Ruined King, will help you deal with any tanky characters you will encounter.
The order after you finish Ruined King, as for what you will buy is entirely dependent on the enemies. How they are building, playing, their capabilities, and composition.
If they're focusing you, and you're having a hard time staying alive in fights, get the frozen mallet, because its passive mixed into your vault will keep them at a safe distance after they used those pesky gap closers. At the end I like to finish up with a Black Cleaver, since because of the new patch changing Ruined King to physical damage, this will eventually reduce their armor by a good amount, causing the passive damage to increase aswell as your overall dps. It also gives some flat penetration, along with a small bit of health, which you may find necessary to stay alive while kiting enemies. End it all with either homeguard, if you're team is having a hard time and on the defensive, or with Furor, since combined with your vault, and auto attacks causing the Frozen Mallet passive, will let you kite almost anyone, for as long as necessary.

Rune Choices, And why they are important.

The reason you're going to get scaling magic resist on your glyphs, is because you shouldnt be worried about mages coming to gank you very early on, and because of this, you have time to level up and eventually get the higher resists than flat would offer, and therefor, when you need it, have more than you would have with the flat resists.

As for seals, you're going to want flat armor since, as said with the masteries, you're going to need them right at the start, as you're fighting the ADC of the enemy team. This being said, you're support should get these aswell, and replace their quints with the gold per 10 instead of using their 9 seals for that. This will keep them alive long enough to be useful early on in lane, and make sure they don't end up feeding.

Marks are fairly straight foward, you're going to want armor penetration marks so that you're able to peirce through most of the armor seals the enemy ADC will have. And they WILL have them, if they know what's good for their champion. This will also increase your total damage output by a significant amound, when paired with your skills and items.

Quints, you're going to want flat AD since as the carry, you will generally start out with around 55-60 AD at level 1, and this will boost it up a bit so that you have a larger gap to play with when lasthitting early on, and making your pokes against the enemy champions that much more effective early on.

Abilities, and why to max out what.

Personally, I like to go with Blinding Assault at level one, because not only is it an AOE damage, but it also gives you 1.5 seconds of extra survivability. Some skills from champions are on-hit effects, and when people do those skills while blinded, it's not going to hit you, and you will survive longer and potentially have the ability to take out one of them early on. After than, you're going to get a point in vault, because it can be used effectively to poke aswell as escape. At level three, get a point in heightened senses if you're support has neglected buying wards, as this will potentially give you vision of that jungler with double-buffs sitting in the rivers brush, and let you get back in time and can proceed to farm up and get that experience needed to carry your team. You're going to want to max out Vault first, since while it scales damage closely to blinding assault, the automatic procc of your passive will make it's damage scale more powerfully for single targets, which as a carry should be your main priority damage type, while blinding assault follows up shortly after, as when you'll have maxed out vault, you should be ending laning phase and teamfights should start becoming more prevalent. Using tag team endgame will give you a massive attackspead bonus when heightened senses is maxed out, and single targets will be easier to take down using the melee form, and you can finish them off by re-activating your ultimate to rain down arrows, killing the target, and injuring anyone that may have came to help them. Or you can stay in the form, to take them down using your skills to keep up with them, and the movement speed, to give you enough mobility to re-enter a fight, or make your way to the rest of your team.

There's only so much variation on what type of mastery setup AD carries normally go, and Quinn is not much of an exception.

The reason I prefer to use these masteries, is because you're not going to use ignite, since in my opinion saving yourself from well over 400 damage lategame is worth more than doing 410 damage over a few seconds, because you're the carry. You're going to eventually have the dps that the damage from ignite is less than one attack on that champion, and because of your damage output, the survivability in a worst-case scenario, will keep you alive long enough to do the extra 2-3 attacks necessary to potentially turn the tide of the fight. You're going to be picking the hp/level and veterans scars for the extra bit of health early game, and lategame. You're also going to need the flat armor since you're going to be put up against an attack damage carry right away, and you'll need that armor asap.