Everyone has a different way to memorise and learn things.
But, like teridax stated, I like to write my quotes repeatedly until I can say it aloud without having to glance at them. In addition to this, getting some one to test you on the quotes is also a good for memorising key points. Ask a friend or your parents.
Also, doing past papers and short responses can also help memorising your quotes and concepts.
Try drawing out a mind map, with your quotes, and place this on your wall. Visuals are also a great way to engage your brain cells with learning. Memorisation can be tedious but every little step counts.
Personally, this is the way I would approach subjects that require quotes (for me, English Advanced) because not only I am imprinting them into my memory (don't know if that makes sense) but it also boosts my self-confidence.