Work with a partner. Sitting by yourself reading lines over and over again can be boring, which is going to distract you from wanting to memorize. Put your full attention into the project by having a partner read lines with you. This is especially useful if memorizing a play or script, but it can also be done for other texts. Switch off reading and re-reading lines from the book with your partner. It will help you to hear and associate some of the text with the voice of someone else.
Write what you have memorized. Writing, not typing, your lines requires significantly more time than simply saying them aloud. If you patiently write down your lines you will not only reiterate them for your own brain in a slow manner it can process, but you will be able to gauge how much you have already truly memorized if you do it without your book in front of you.
Create associations with the text. Your brain will remember words like it remembers events. It brings them back to the forefront of your memory when something (a smell, sound, key word) brings about a trigger. Play some light instrumental music in the background when working on a particularly difficult piece of text. Bake cookies or pie while you recite lines. Sing lines that are usually spoken. These sensory triggers will help you recall the information in the future.
Understand what you are reading. Memorizing words without fully processing them will make the job even harder. If you get stuck on a word, however, you may be able to trigger the next word if you know where the text is headed. This comes from reading and understanding the material.
Start with easy texts, and move to more difficult ones. A book will be filled with many parts, some easy and some hard. Trying to work from start to finish if the beginning is difficult may be setting yourself up for failure. Try an easier section to boost your confidence and productivity at the start before trying harder chapters.