Start from the last line of the passage and work backwards. This is an appropriate method if you are memorizing a single passage, such as a speech or monologue. If you start memorizing the final sentence and memorize each one preceding it, you will end up equally familiar with the entire passage and will not forget the second half as you recite by memory.
Listen to the passage. Reading aloud and repeating is helpful, but listening multiple times can help passively "imprint" the passage on your mind. Record yourself reading the passage and listen to it as you drive or do chores.
Break the passage into sections and number them. Memorize each passage on its own as a smaller task then add them together to form the larger passage. If you know how many pieces of the passage you need to memorize, you can count them off as you recite the passage in its entirety and will be less likely to forget important parts of the passage.
Practice the completed project in front of an audience. Become accustomed to reciting the passage by memory under pressure; simulate the actual event so your nerves won't affect your performance when you give your presentation.