Read the script straight through and highlight your parts. Do not try to memorize any lines at this point; just try to get the main idea of the play.
Read your part out loud, since you will perform it this way.
Get a friend or a family member to read the other parts in the script and listen for your cues. Recognizing the lines of your fellow characters will help prompt you to remember your own parts.
Rehearse your blocking -- your movement in the play -- while you recite your lines. If you memorize your blocking and your lines together, they may cue one another for you on stage.
Memorize your part in pieces. Do not try to remember all your lines at once; break up the process by act or scene. If you have a rehearsal schedule, memorize your lines in the order that you will be rehearsing them.
Be aware of patterns in the text, such as rhymes and repetition. Pinpoint the important words first and then try to remember the words that connect those words.