Asking for permission to use a copyrighted work involves several steps:
Keep in mind that what you are getting from the copyright owner may not be a perpetual license, but a license to use a work in a particular situation, possibly for a limited amount of time. Should you wish to repeat this use, or change the conditions under which you will use the work, you may need to request permission again.
The copyright owner is entirely within their rights to ask you for a fee or to say no. These fees may or may not be negotiable.
Published Works [books, journal articles, published music] :
The key to making a good request is being explicit and precise.
The Copyright Clearance Center (CCC) can provide licenses for uses exceeding Fair Use. The CCC specializes in academic uses such as course packs, e-reserves, etc. Their pay-per-use permissions page lists these services and provides links to set up accounts.
Course packs created through Brown University's Graphic Services are all properly licensed.
Columbia University Copyright Advisory Office. Asking for Permission. Columbia's site offers practical advice on how to contact the copyright owner, how to write an effective letter (email) and how to document your efforts. It also includes model letters for use of video or text, and for use of copyrighted materials in a course management system.
Stanford University's The Basics of Getting Permission includes useful advice for seeking permission, getting it, and negotiating payment (if required).
Sometimes it is not possible to get permission. The copyright owner may choose not to respond. In some cases this may be because the owner's records (often a publisher) either have been lost or destroyed by merger, fire, or conflict. It may not be possible to identify the copyright owner, e.g. the publisher has gone out of business, or the creator is deceased, and there is no clue as to who owns or controls the estate of the creator. Or, the copyright owner may have quoted a royalty fee of extraordinary size, or perhaps simply said no. You still have options: