How can I find out who owns a copyright?

You can research the records of the U.S. Copyright Office. But that only covers registrations of copyright, not all copyrights.

“The U.S. Copyright Office can provide you with the information available in their records. A search of registrations, renewals, and recorded transfers of ownership made before 1978 requires a manual search of their files. Upon request, their staff will search their records at the statutory rate of $165 for each hour (2 hour minimum). There is no fee if you conduct a search in person at the Copyright Office. Copyright registrations made and documents recorded from 1978 to date are available for searching online. For further information, see Circular 22, How to Investigate the Copyright Status of a Work, and Circular 23, Copyright Card Catalog and the Online File.”
— U.S. Copyright Office