Copyright registrations and renewals covering the perioed 1870 - 1977 are accessible through a physical card catalog housed in the Copyright Office and also through a virtual set of volumes titled the Catalog of Copyright Entries which cover the years 1891 to 1977.
The Copyright Office offers a tutorial.
A Guide to Searching the Catalog of Copyright Entries
The Online Books Page, hosted by the University of Pennsylvania Libraries, is a website that facilitates access to books that are freely readable over the Internet. It provides access to Copyright Registration and Renewal Records. Records may be searched by year, 1899 -present and 1870 - 1890 for dramatic compositions only. This site also provides links to other indexes allowing access to copyright records.
Google has scanned 91 volumesof the U.S. Copyright Office Catalog of Copyright Entries (including works registered from 1923 - 1978.) and made those volumes searchable online through Google Books. Google Copyright Search provides access to the Catalog of Copyright entries, allows searching over all 91 volumes as well as over individual volumes covering registrations in or around a particular year. This website also includes helpful tips on copyright searching.
Copyright registrations for all works dating from January 1, 1978 to the present, as well as renewals and recorded documents, are accessible through the Copyright Office Online Records Catalog.
The Copyright Office offers a tutorial, Guide to Searching the Copyright Office Catalog, on its website.
The U.S. Copyright Office offers a search service for persons interested in investigating whether a work is under copyright protection, and if so, the facts of the copyright. For a fee of $200.00 per hour or fraction thereof (2 hour minimum), the office will search its public records and provide a report of its findings. Based upon the information provided the Copyright Office will provide an estimate of the search fee.
The links below will connect you to information about how to search for the copyright status of a work.
Researching the Copyright Status of a Book - Columbia University Libraries
Searching the Copyright Office and Library of Congress Records - Stanford University Libraries
How to Investigate the Copyright Status of a Work - Circular 22, U.S. Copyright Office