Quinn is weak early in the game, but when she reaches lvl 8. She starts to rise above other carries.

Focus on creep killing.
Stay passive until jungler ganks.
Quinn works with patience.
Quinn has the greatest counter initiations.

Grab what you can. You shouldn't devestate half your health for a single minion.

Quinn works well with champions that have Crowd Control, Gap Closers, and some defensive mechanisms.
Examples: Leona, Thresh, Shen, and Taric.

Sustain should be your own problem, but Shen can help you by marking enemies healing you on your own Basic attacks. Items that build into "Face of the Mountain" will be great for your support to pick up.

Good fragile supports

Sona will be your best friend at lvl 6. When she gets her ultimate. You could comeback the lane by bursting down the ADC full offense.

Quinn's E should never be used while farming; Although Q is a decent utility to farm with when cheap.

Execute squishy isolated targets where you have vision.(Wards)
- Do this by getting to them with your Ultimate(If they are nearby)
-Then(In ulti form) Initiate with your E follow up with Q then the passive attack speed from W should shred them down for the Execution with your Ultimate.
-BEWARE: Do not chase enemies into blindspots no matter WHAT.
^Quinn has little escape mechanics when your Ultimate cant give you the 90% MS buff. So if you get caught- there will be little to no escape.

Quinn is best when your team GETS initiated on. She works well with champions like Wukong and Leona as her support. Lets say Jarvan IV uses his ultimate on you. Your reaction MUST ALWAYS be to use E to jump out into the rest over your team. OR, you can cancel his ultimate before the Cataclysm even appears by using E to knock him back.

Quinn, unlike most other AD carries, has a displacement spell- Her E "Vault". Her E can cancel things like Shen's ultimate, Jarvan's Ultimate(To be recasted later), Fiddlesticks's Ultimate or Drain, Caitlyn's ultimate--and when timed well Caitlyns Peacemaker.

Vault can allow you to follow people like Kassadin or Leblanc who have jumps( Even Tristana, Caitlyn, and Corki). This ability surpasses the summoner spell Flash.
BEWARE: May cause unintentional diving into the enemy team with no return!

Her R-E-Q combo can devestate single targets

Clearing large minion waves with her Q then R active can change the fate of turrets threatened by them.

Quinn's W, Heightened Senses is great when enemies flash through walls and you can catch them with vault. As much as this can help, it'll be your downfall-- As you use this ability, it creates a circle that covers a bit less than the circumfrence of your vision, enemies can see this. This aspect can give you away, your enemy(ies) will either make Flight...or Fight.

Lets say you catch someone taking their blue with Heightened Senses. Also, you have 20 kills and its 30 minutes in. They have no turrets in the vacinity. They will either try to hustle their blue and risk dying, fight you into their inevitable death, or run square out of there. However..
Lets say you had 2 kills and its 15 minutes in, your team took dragon and you have a BF sword paired with dorans blade and Boots of Speed. The enemy team is missing their mid turret but they have Bot to be cleared. The enemy jungler has 4 kills, but lets say he doesn't recall your score. Ever. Creep score is even. The jungler is low though. They will either back off, or take blue anyways, ignoring you. You have the chance to make the difference in the game. Get the shut down on the jungler, or die in the off-chance that their ADC was around the corner. But see, the best thing to do is not make the choice, but leave to fight for better chances later. Quinn is greatest played with patience and a positive attitude. When the time comes, strike, but strike HARD.

Trinity Force:

If we do the math... Spell blade on Tri Force deals Physical Damage equal to a Critical Strike...
(200%)...On top of a critical Strike.. The Damage will be 400% greater then the origional basic attack. Harrier deals damage that we can round to about 200%(Equal to a Critical Strike).

So the damage of Critical Striking off a Vault(Your E)[Applying Harrier] Will be 600% physical damage compared to the origional basic attack.(100%)

Last Whisper:

I prefer this item over Black Cleaver because you are basically giving up 10 attack damage for 15% Armor Pen. for about 1000 less gold.

Blood Thirster:

I prefer this over Blade of the Ruined King because:

1. The end build does better with the greatest amount of attack damage possible(Hint for many Fortification{Red} Elixers late game.)
2. Quinn's abilities scale better with more damage.(Your Marks should be the base of your Armor Penetration.)

Pros:
-She can devestate single targets
-She can Kite really well with mobility from furor, harrier, and Phage passive.
-Her E can be a gap closer and maker.
-Her Q is a great dueling utility against enemy ADCs.
-Her ultimate active can execute Duplicates and Origionals without many problems( Wukong, Leblanc, and Shaco.)
Cons:
-Low range
-Weak early game
-CC not for me

Play Safe Stay positive :)

Quinn will be very frustrating unless you keep a positive attitude. Good luck future Challengers!