If your intended use of copyrighted work is not covered by Fair Use or one of the exemptions, you should seek permission from the copyright owner.

1. Identify the Copyright Owner: In academic publishing, the author may have transferred their copyrights to the publisher. Be sure that you are seeking permission from someone who can actually grant it.
2. Contact the Copyright Owner: Publishers may have instructions or a contact posted on their website for securing permissions. There are also companies that license work a group of holders, such as the Copyright Clearance Center. You will want to detail the specific work you are referencing and any and all planned uses of the work.
3. Keep a Record: If you are successful in obtaining permission, keep any of the related correspondence. If you are not successful in obtaining permission, you may want to still retain related correspondence to demonstrate a good faith attempt to contact the copyright owner.

There are several excellent resources online that identify potential copyright-holding groups, provide sample request text, and other guidance for obtaining permission:

In some cases, audio or video works can be purchased with Public Performance Rights (PPRs), which license the right to perform the work in public beyond the narrow classroom exception. Very few films, including only a small number held by the Furman University Libraries, are already licensed for public performance. PPR licenses can often be purchased from vendors or from the distribution company (most documentaries or independent films). 

Resources

Here are a list of organizations that hold PPR for many films. We recommend starting with Swank.