Highlight your lines. This forms a strong visual connection to the script. Try highlighting in alternate colors, or using a different color for a particularly difficult passage. The bright colors will help the words stick.
Read out loud. Vocalizing and hearing the words engages more of the brain than reading silently. Practice saying your lines in different voices and with different inflections. This variation helps keep you mentally engaged. Tape record yourself reading, and listen to the tape throughout the day.
Break the script down into manageable chunks. Tackle a lengthy speech by reciting the first four or five lines until you can say them without looking, then move on to the next four or five lines, and so on. Likewise, work on and memorize one scene completely before moving on to the next.
Practice with a partner. Ask your partner to stay "on book" and give you your cues while you practice without the script. Instruct her to correct your mistakes. It might also help to hear someone else reading your lines aloud.
Recite your lines with movement and gestures. Walk through the blocking you'll use on stage, and visualize delivering your lines to your fellow actors. When you say the words, think of your character's motivation and emotions, and the purpose this particular line serves in the play. Fully apprehending the script mentally, physically and emotionally will cement the lines in your mind, so delivery will come naturally.