First, determine if you are dealing with a copyrighted work. Generally works created prior to 1923 are in the public domain. See the public domain tab to learn how to identify works in the public domain.
If the work is copyrighted, your next step is to:
If the work you wish to use is not licensed or covered by an exemption, you may run a Fair Use analysis. See the Fair Use tab.
If none of the above allows you to use a copyrighted work, then you can seek permission which may involve paying royalties.
Kevin Smith, Fair Use of Movies & Music: Managing Copyright in Higher Ed, 2010