How should I learn quotations in a closed-book exam?

Depending on the type of learner you are, you can learn quotations in a number of different ways. There are three main types of learning - kinetic, visual, and auditory. Now, if you are a kinetic learner, I suggest that you move around whilst learning your quotations, or you could even make gestures that remind you of the quotation you are trying to learn. If you are a visual learner, I suggest that you write out your quotations, maybe even colour code them - this way, you will be able to picture, or 'visualise' the quotations in your head, making it much easier for you to write them down in the exam. If you are an auditory learner, I suggest that you say your quotations out loud; another way to learn them could be to record your quotations and listen to them on repeat, in your spare time. A really useful site that I used for my English A-Level, and even other subjects, for learning words or quotations was 'Quizlet' and 'Memrise'. On these sites, you can not only add your own sets of flashcards and classes, thus tailoring your learning to your specific subject, but you can also find flashcards and classes that others have already made and use those, as long as they are in line with what you are studying.
On the practical side, I would advise you not to try and learn huge chunks of quotations for your exam: you are more likely to get confused, and even quote something inaccurately. Instead, try to pick out key words from the original quotation that you can embed into your sentence, that is, short quotations. Using this method, your sentence will flow naturally, as the quotations are embedded within the sentence, and it will read much more fluently. Fluency is not the only useful aspect of embedding short quotations - this method demonstrates, to the examiner, that you can specifically pick out details from the text, and use them accordingly to support your thesis/line of argument in your essay. Also, embedding short quotations means that you are much more likely to include relevant and accurate quotations from the text.