Find the copyright's owner. All copyright records after 1977 are available online (see resources). For registrations made before 1978, you will have to consult the copyright card catalog in-person at the fourth floor of the Library of Congress James Madison Memorial Building in Washington D.C., or call and pay a Copyright Office staffer to look it up for you.
Determine if the copyright is still valid. According to the U.S. Copyright Office, if the work was created after 1977, the copyright is valid from creation until 70 years after the author's death (if multiple authors, it's 70 years after the death of the last living author). If the works are done by a contractor "for hire," the copyright lasts 95 years after publication or 120 years after creation, depending on which is shorter. If the work was created before 1978, the rule was typically 28 years from registration of the copyright, and copyright holders had an option to renew it up 67 years longer.
Contact the owner of the copyright. Let him know that you're interested in purchasing their copyright from him. If he's agreeable, negotiate a price.
Transfer the copyright. A transfer is not valid until a written contract is signed by the person giving up the copyright. The Copyright Office doesn't facilitate the transferring of copyrights, but it will record a the document of transfer and keep it on file for future verification purposes.
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