Dorans for safety
Long Sword for extra cut down damage
Cull for Scaling and extra Cut Down Damage
Garen's R range: 400
Garen's Skill Max Order: E → Q → W (some Garen's go W max to survive this lane)
Level 1: Auto him from the bush, but don't E him instantly. Instead, wait for your passive to mark him from the bush, then auto him and see how he plays. If he runs away, then E him to chase. If he Qs you to run at you, instantly E him because your E cancels his Q, which is what makes this matchup unplayable for Garen.
Note: when you Vault garen during his Q, his auto and silence are canceled, but he still has the ability going. He can still get his silence off, but it's very unlikely unless he flashes on you. Save your E strictly to cancel his Q in lane and you will make him cry.
Level 2: Garen will have E or W, depending on how low he is. Level 2-5 are the same, save E to cancel Garen's Q and then constantly auto Garen whenever he walks close to you. He'll get fed up and try to Q engage on you, and then use your E to cancel this, then auto him to death again. If you only use E for this, then Garen can't play the game. This is one of the biggest counter picks in all of League of Legends.
Level 6: If you anticipate death from Garen's only outplay against you (which is Garen flash Qing you and spinning on you, for example, and you're low enough to die to his R) What you will do is you will Q-E Garen instantly, which will blind him and push you out of his nearsight vision radius. Garen's R is cancelled if you leave vision, and this concept works if he's blinded. If you vault out of the nearsight before or as he Rs you, then his R animation will go off but it will be put on a 2 second cooldown and won't do damage to you. Otherwise, if you are low and anticipate an R from afar, just blind him, auto for harrier speed, and then run: he won't be able to click his R on you since it's point and click.
After Garen's mini rework, the matchup is heavily one sided towards Quinn's favour.
The main thing to note is that now Garen's Q is programmed as an auto attack, which means that Quinn's E, Vault, can cancel the damage AND silence from Garen's Q, Decisive Strike.
You should play the lane extremely aggressive and auto attack Garen whenever you can to proc your PTA every time the PTA proc is off CD.
The only thing to watch out for is to only use your E to counter Garen's Q.
Whenever Garen presses his Q ability, you should react immediately with your vault because he loses the movespeed bonus when it's cancelled.
Keep in mind that his Q is an 8 second CD while our vault is 12-8 seconds, so he will have it up before your vault is up basically every time.
To maximize your effectiveness in lane, play back a little bit when your vault is at arround 4-6 seconds if you vaulted his Q in an earlier trade to prevent the good Garens from silencing you before your vault comes back up.
Post level 6 the only thing you need to know is that Quinn's Q can cancel Garen's R lmao.
How this works is if you blind Garen and you leave his nearsight vision radius when he presses his R ability, his ult animation goes off, but the damage is cancelled and his R is placed on a very short cooldown.
Keep in mind that his R will be back up in a matter of seconds, so if you are able to pull this cancel off, then don't get greedy and overextend because he will have it back up momentarily.
You outscale Garen incredibly hard, this is a dodge worthy matchup for him and arguably the biggest counter pick in all of League.