For the first part of this question it is important to think about key themes and characters and group your quotations accordingly. Don't try to learn whole passages. More often than not the shorter, memorable quotations will actually be more significant. Also learn quotations that can be used to validate a number of points.
Flashcards are my personal favourite. I always colour code my quotations according a theme or a character. I have also recently started to use the app quizlet and I know other people who use memrise.com. Quizlet is a great app because you can group quotations into folders, and be tested even when on the move.
Learning the very beginning of each quotation is important because it can act as a springboard.
Sometimes putting quotations to a rhythm can be useful. I know some people who have made up whole raps.