Take dance classes with new instructors. This will give you practice trying to learn choreography in unfamiliar environments, preparing you to do so for an audition. Dancers taking classes with the same instructor repeatedly often don't go outside their comfort zone.
Learn as many basic steps as possible and the names for them. Many routines contain combinations that are standard and well-known. Being familiar with these will cut down the number of new steps you have to memorize at the audition.
Learn the choreography ahead of time, if possible. Some well-known shows, such as "Chorus Line" and other Broadway shows have set choreography that doesn't change.
Watch the choreographer closely while she is explaining the step. Don't attempt to do the steps yourself until after she has completed the entire routine.
"Mark" the steps the second time the choreographer goes through them. Marking is completing the steps without full-on energy. Increase the energy put into the steps each time you go through them and begin to feel more comfortable repeating them.
Break the choreography into sections in your mind. This will help you memorize the steps. Give these sections your own names that will help you remember them.
Use the music to help you remember the choreography. Use parts of the song, such as strong beats or pieces of lyrics, and associate them with their corresponding steps.