ilikepapaya Flashcards, is one way to go about it. Another way I found helpful was to understand what the quote meant. Then I'd randomly send it to a friend, and they'd be like, "Dude, what the heck does that mean," and you give them an explanation.
Saying them out loud and getting into the character who said them was also a really fun way to remember them. My class is doing Macbeth for English (QCE system btw), and I'd randomly just say something like "Stars hide your fires! Let not light see my black and deep desires” - Macbeth. I do this in my room, where no one can see because it is slightly embarrassing, but it works.
When your on the bus, train, or in the car, listening to the quotes on repeat really help engrain it in your brain. Even if your not fully paying attention.
Also, memorising quotes that work for multiple themes is just more bang for ya buck.
Hope this helps,
-jinx_58