Sign up for periodicals and websites that list casting opportunities, such as Backstage or Actingbiz. Consider joining the Actor's Equity Association for listings of casting calls.
Research the show for which you will be auditioning. Decide which characters in the program you may be suited to play. Although you won't necessarily be auditioning for a specific part, it will influence the type of song you prepare.
Choose a song to prepare for the audition. Find a song from a similar musical that is sung by the type of characters you think you might be suited for in the show. Make sure the song is in your vocal range and that you can act it and sing it.
Practice the whole song, even though you'll only be expected to sing 16 measures. You will likely have to sing the whole piece if you are "called back." Also prepare a 1 or 2 minute monologue, depending on the casting requirements.
Prepare a resume of your acting and singing accomplishments. Include three sections on the resume: Experience, Training, and Special Interests and Talents. Staple a head shot to the resume. Bring three copies of the resume/head shot with you to the audition.
Arrive at the casting call at least an hour early, as the lines tend to be long. Bring a bottle of water and snacks with you in case you have to wait a long time. Also, bring the 3 copies of the resume/head shot, as well as sheet music and dancing shoes if you are required to dance for the audition.
Greet the pianist and give him your sheet music when it is your turn. Introduce yourself to the auditors, stating your name and the title of the selection you will be singing. Give them the copies of your resume/head shot.
Thank them after they dismiss you. Hope to receive a callback, which can happen anytime from that day to a month later.