The brain communicates with images. You may find it easier to remember images than to remember abstract symbols, such as words on a page. Visualization can make memorization faster. With this method, the actor needs to associate an image with every line or phrase she has to learn.The more outrageous the image, the easier it will be to remember.
For example, the line "Why speaks my father so ungently" from "The Tempest" could be connected to the image of the actor's father yelling. Rocks fall out of his mouth with each word and squash the actor's boyfriend or girlfriend. (Using real people in the fantastical images is also helpful.)
Another visualization technique is for the actor to picture the scene in the play through her character's eyes. She should imagine in detail each element in the character's surroundings. Other senses should be involved too. The actor should imagine what the character is smelling, hearing and touching while the lines are being spoken. Creating the sensations that go along with the words can improve the actor's ability to remember them.
Writing or typing his lines is another way for an actor to memorize his part. The act of transcribing the lines makes them easier to remember.
The actor can also record the scene he is working on and listen to it before going to sleep, or while driving or exercising. A variation of this technique is for the actor to record only the cue lines---the lines that come directly before his own lines---leaving time between them. With this method, the actor doesn't just listen to the lines. He fills in the missing lines.
Instead of recording the cue lines, have a friend or family member practice with you by reading the cue lines. If the actor misses a line or says it incorrectly, her partner can correct her immediately. Before moving on, the actor should say the line correctly several times.
Some actors find it useful to read over the lines silently again and again. Others feel that forming the words with the lips is key, even if the words aren't spoken aloud. Still others find saying the words aloud is the best way to memorize them. An actor can make flash cards for herself, with the cue line on one side and her line on the other.
The actor needs to understand each line that he is memorizing. This means looking up any unfamiliar words, but more importantly, it means understanding why the character is saying the lines. The actor needs to know what the character is hoping to accomplish. It will be easier to remember the lines once they are meaningful emotionally.
The actor should start memorizing her lines as soon as she gets the part. With the lines learned, the blocking---movements on the stage---will be easier to remember. Rehearsal time isn't for memorizing lines. It's to work with the director and the other actors.