List your goals for finding a composer for your film. Clearly stating and recording your goals can help you plan how to achieve them and judge how well you succeeded.
Ask your friends. Filmmaking, like many art forms, depends largely on personal relationships. Your friend from film school or the woman who runs your favorite camera rental store may know of a composer who suits your needs.
Attend film festivals. Most major metropolitan areas have several film festivals open to the public. Many of the films shown at festivals feature scores by talented, ambitious but as-yet-undiscovered composers. Talk to the filmmakers whose films' scores you enjoyed, and they can help put you in touch with their composers.
Solicit submissions from local universities. Institutions of higher learning have a wealth of young, highly trained composers looking to hone their skills and develop their oeuvres. Unlike more seasoned composers, students may work in exchange for credit or experience.
Contact the American Society of Composers, Authors and Publishers (ASCAP). ASCAP helps connect composers with job opportunities, and their website has a wealth of information on how to find a composer for your film, standard rates and usage rights.
Use an online scoring site. Many companies connect composers with clients via websites where composers may submit scores on spec to filmmakers. You can submit your film to one of these sites and choose from the composers who submit their work.