Determine whether the music's usage constitutes new artistic expression or meaning. This guideline is especially important if you are planning on filming a personal reproduction of the music using a band or solo artist; just because the original band isn't playing the song doesn't mean the lyrics and music are not covered under copyright law. If you have substantially changed the music to exhibit a new, personalized expression of ideas, then you're within your legal rights. Additionally, if using a portion of the previously recorded music changes the original meaning or expression, you're also covered.
Consider the length of the piece. Stanford University's Copyright and Fair Use Center offers this advice: "the less you take, the more likely that your copying will be excused as a fair use." However, Stanford also cautions that even a small portion is inexcusable if it is taken from the "heart" of the work---in other words, do not take the most recognizable or memorable part of a song.
Determine whether your use of the music has educational value. While mass distribution of educational pieces still requires permission, one-time classroom usage is generally considered acceptable according to the Video University article "Copyright for Video Producers."
Determine how your usage will affect the musical piece's sales. If your usage will have any negative impact on the musician's income, you are not allowed to use the piece.
Cover your bases by consulting a lawyer or submitting the clip to the original artist for approval. If the musician is able to see that you've used only a very small, inconsequential clip of the work to add to your artistic vision, he or she will not object to the usage. Even if you are fully covered via fair use, it's always a good idea to get the artist's approval to avoid potential lengthy and costly court cases (even if you win those court cases in the end).
Seek permission for usage of entire songs or large clips of songs. If you know you're not covered under fair use, you can still use the work if approved by the copyright holder---usually the musician or record company. Stanford's Copyright and Fair Use Center recommends sending usage requests at least 3 months in advance. Formalize the request process by sending a well-produced, notarized letter on resume paper; do not converse over e-mail, as hard-copies will hold up better in court if the copyright holder ever tires to back out of the permissions agreement. Even with advanced permission, be prepared to pay royalties or one-time fees for popular songs.