Double proc of Quinn's passives.
Auto attack resets from E and Ulti.
Triple proc of Quinn's passive.
Using E to escape over terrain (Attacking wolves to pull them then E over the wall).
Ghost procs.
Vault through Ulti - Reproccing Ulti mid E.
E to follow enemies flash.
E > R > Blade to disengage.
Using R > W/Ward > E to escape to jungle camps.
Cancelling Thresh lanterns and channelled abilities with E in both ranged and melee form.

In standard lanes, I nearly always start with Q and a Doran's with 1 pot. If you can get to lane early you should try the "Dominate from Level 1 Trick" (See Video). This involves you establishing an XP advantage with damage on the creep wave, timing your approach when the caster minions AA and when the enemy laner goes for a CS and trading between the enemy creep wave and the enemy. Even if the trade goes poorly (unlikely) you have the zone advantage and the XP advantage to hit LV 2 first and continue your aggression.

You should try to attract the attention of the enemy jungler with your aggression and use your 1v2 potential to your advantage (See Videos). It is important especially when playing top lane to MAKE SURE YOU GET LEVEL 3, try and use your jungler as a mirror +/- of where the enemy jungler is. You can tell your jungler to continue farming or ganks other lanes once you are comfortable in the 1v2. It is simply about orb walking, use of bushes, summoners, turning at the right time, use of your minions and correct rotations of CD's. It 100% comes down to experience and the video should help for sure.

Regular double proc pokes into Q are core. When going for tower dives around Lv 3 remember to Ignite during the flight of your E rather than after. It is likely they will flash before you proc the passive or just after, thereby preventing you from Igniting after.

You will gave Ignite up on your lane in most match ups which gives you pressure, however you need to be careful in some match ups to not force your laner back too early, or you will be at a disadvantage (pots wise) with an instant TP. (It is important to force Ryze to TP before tear though).

The basic way the lane should work is aggression, poke extended trades. Get Brutaliser and 6 and look to roam. Either push out your lane and gank through the lane for bot or go via the jungle / river.

Core Items Early = Brutaliser, Boots, Double Dorans, Bilgewater

The mid game is orientated around rotating between Pressure in lane (if you are able to still lane - sometimes you may need blade before you can continue to lane) > making a pick / roaming > Back into Pressure in lane.
At this point your assassination potential is at its highest and you should familiarise yourself with some of Quinn's post ulti combos:

Ulti > E > AA > Q > AA Blade Ignite > Ulti > AA Reset from Ulti (Blade and Q are interchangeable depending on the situation)
Double Proc of Passive in Ranged form > Ulti (Your E will still be CD) > Use your Ulti as a ranged assassinate or Blade/Flash Q > Ulti AA Reset.
Ulti > E (MID FLIGHT OF E) > R to get the damage and assassinate but Vault back from your target (See Video).
Be aware of when you have to save your E to chase enemies escapes e.g Ezreal El; you will simply Ulti all the way to him and E after he does.
Be aware of your potential to jump over terrain with a well positioned E, as well as following enemy flashes with E. Also practice using close range E > Blade > Ulti to escape and using your E to minions during Valor form if they continue to chase.
You have a lot of Split Push pressure at this stage. USE THE FOG OF WAR AND BUSHES WELL. If you push a lane someone will come to defend it and die (if you wait for long enough in a bush), if not you can simply continue to split and catch someone on the rotation to defend OR Ulti to join a teamfight mid game.

This is when people think Quinn falls off or when she is forced to split push. Quinn's role late game can either be Splitting, making a pick or teamfighting.

Similar to Zed you have great assassination potential, it is a lot easier for you to burst a target without them escaping (More catch potential and mobility /they cannot QSS Quinn's damage). Often people wont be able to react to the damage in time to peel and you can easily burst through heal,flash and blade. (See Video for Teamfight potential). Unlike Zed the disengage of Quinn after you assassinate your target(s) is slightly harder without practice. The perma move speed from the build, timing of the assassinate and monitoring your own CD's with mindfulness of the transition after during your assassinate all help. e.g You know you can kill this target now but do you need to stay in Valor for slightly longer to get CD's up for the disengage. Once Quinn leaves the team fight her perma move speed, kite, chase potential, CC from E and double/Triple proc passives make her a menace for the enemy to deal with.

You can simply use your Ulti in the vision of the enemy and circle around a "dangerous" position, forcing the enemies to commit peel and CC in anticipation of your engage. Thereby winning a teamfight by doing "nothing".

You can also stay in ranged form and peel for your carries at the start, if the enemy engage is split and unorganised, you don't want to become too separated from your team diving the back line. Use Q and E to peel for your carries saving your Ulti for later in the fight.
Your items should look similar to above and the damage by no means falls off at all with this build (See Video). The build can vary as discussed before with the option to sell boots.

Split pushing again is an option and your global pressure with Ulti means that it is incredibly hard to deal with your. You push waves fast, are unteachable, unduelable and most champions with clear (Zigg's) are easily dove by Quinn. She also retains her 1v2 potential at this stage of the game.

You options are always open and decisions come through experience. Watch the 2 inspirational videos and make Quinn fit your playstyle.