So, you have determined that the work you want to use is probably not in the public domain, and that it is not available under a Creative Commons license (or that your use is not covered by an existing license). You don't think your use is covered by any of the exceptions or limitations, including fair use (or you just feel unsure whether your use is a fair use.) You may still be able to use the work, if you seek permission!
The U of M's Copyright Permissions Center provides assistance in acquiring permissions for materials to be copied for course packets, library reserves, course websites, and other University-related purposes. If you need permission for a personal use not related to University business, you may need to contact the copyright holder yourself.
Keep in mind that many creators do not themselves own their copyrights - the copyright in most books is owned by the publisher; the copyright in most music is owned by a distributor. However, it can still be a good idea to contact the creator - they may be able to give permission, and can usually put you in touch with other rights holders if necessary!
Sometimes it is difficult or impossible to identify the copyright holder for a particular work. It may be possible to identify who owned the rights at some point in time, but after a creator's death, or after the dissolution of an organization or company the trail of ownership may disappear. These works are referred to as "orphan works" - and there is no way to get permission to use them!
Orphan works are often unique, rare, or hard to find - the collections of Archives or Special Collections Libraries may contain high percentages of orphan works. These works present real challenges for users - who must either accept the risk that a copyright holder may later identify herself and object to a use (a risk that is lessened when the work is potentially in the public domain, or when the use is potentially fair), or give up the plan of using such a work. Many publishers and distributors require explicit permissions when quoting more than tiny amounts of any work; creators may have to work very hard to persuade them to allow inclusion of an orphan work.
Orphan works are a real problem in copyright law. Legislation has been proposed several times that would address some of the problems, but it has never been passed.