See lots of movies. Choose well-known classic films as well as highly rated contemporary ones. Films that won awards or create media buzz often have great quotable lines.
Watch films on DVD or video with paper and pen handy. See movies written by top screenwriters multiple times because you can't catch all their great lines just from one viewing.
Review the quotes you've chosen after you've let some time come between viewing the movie and writing them down. Cross out lines that don't appeal to you on second reading.
Journal about the meaning of the quotes if they're profound. Some lines you like just because they're funny, but the ones that you'll remember have a kernel of truth about life and human nature.
Practice writing them over and over so you remember them. When you find yourself phasing out on the words and writing the quote automatically, you've memorized it.
Choose your occasions carefully. Quotes can make a great impression on an audience or emphasize a point in a discussion. At informal gatherings, they'll just make you sound weird.
Take care the movie quote is really appropriate for the situation. There's nothing worse than saying a line that makes your listener wonder why you bothered.