I'm not allowed to bring books into exams, how do I learn them off by heart?

First thing to say is: don't panic. This does't mean that you have to know the whole text off my heart. In fact, if you did, the chances are that you wouldn't use quotes concisely enough to make your argument and score higher marks. You'll know the texts well enough to paraphrase in most cases, but do make note of the really important ones. For example, Hamlet's Act 3 Scene 1 soliloquy is so famous it wouldn't look great to an examiner if you didn't know it word for word. Also, do try to memorise a few quotes that will lend themselves well to multiple themes - that way, you'll also make sure that you understand the quote and can analyse it properly in your essay (spider diagrams are a great way to do this - see whiteboard). You'll need to prove to an examiner that you can understand language and how it works, so do close read your chosen quotes well in advance before you go into the exam room, so that you can prove to the examiner that you know your literary terms.