Pay attention to the other parts in the play. Don't just listen for the parts that appear before you come in. When there is a dress rehearsal, stay the entire time and watch the play. Learn about the context in which your character exists in the play. Often, a performer will only stay for his section of the play during a rehearsal. Study your lines while watching the rest of the play.
Listen carefully to the lines that come immediately before your own lines. In the early stages of learning the play, you will usually be able to use your script. Try to look at the script as little as possible to make it easier when it comes time to leave the script at home.
Break your lines into small segments. Instead of trying to memorize one sentence at a time, memorize the sentences by breaking each sentence into two or three parts. If the sentences are short, just memorize one sentence at a time. Build each sentence and part onto the next part by completely memorizing one part before moving on to the next. Type out your lines three times each. The act of typing your lines makes you focus on the words. At this point, type each paragraph three times before moving on to the next paragraph.
Stand in front of a mirror and watch your lips as you read the lines. You will find that in a performance, if you can recall what your lips looked like when reading a line, you can often recall the words. This technique works extremely well. Practice recording your lines with an audio recorder. Using a tape recorder helps recreate the sensation of performing. You can also use it to record the entire rehearsal with your fellow actors to help with your practicing. You may also record other people's lines and then play them back to help you memorize your lines.
Find family members and friends who will read other parts with you and help you memorize your lines. Give each member a separate part, and have one person hold onto your script to help you in case you forget a line. If you forget a line, she should provide you with hints to try to get you to remember the line. This is more effective than simply reminding you your line.