Visit free music and sample archives. Sites like Incompetech, Looperman and Shockwave Sound contain free audio samples and full-length songs intended for royalty-free use. Browse the archives and find music that suits the mood of your film. When you find a song that you want to use, read the description page to verify the terms of use, then click the "Download" link. Some sites require you to right-click the song title and select "Save As."
Download music from the public domain. The non-profit organization Archive.org is the Internet's largest database of public domain material. You can find free music by visiting the site and clicking "Audio." The Library of Congress also features public domain sound recordings on its American Memory page, while MusOpen and Project Gutenberg host many recordings that have fallen into the public domain.
Create your own music using royalty-free samples. You do not need professional recording abilities in order to create custom, professional-sounding music: just install a free multi-track recording program like Ardour, Audacity or QTractor and download free loops from a website like Loopasonic, Looperman or Flash Kit. Open your software, drag loops into the program window and arrange each loop on its own "track," or layer, on the time line. Layer the loops on top of one another to create completely free customized music.
Inquire about music on online musician forums. Create a new forum topic and explain that you need music for an upcoming film. Explain that you cannot afford to pay for the music, but will provide full credit to the artist. Many aspiring and rising artists will leap at the opportunity to have their music featured in a film, and will gladly share their music with you. Harmony Central, Sputnik Music and Gearslutz are three of the most active musician forums on the Web.