Look inside the front cover of the book. This will reveal who the publisher is and the date the copyright was registered. This date should not be confused with reprint dates that refer to the rerelease and/or repackaging of the original text. If the edition predates 1963, your homework is to find out if any new editions were published after that date. The quickest way to check is to go to Amazon.com and do a title search. Don't assume, however, that a book published in 1951 that doesn't show any subsequent editions wasn't copyrighted; it may just not have been published after its renewal by the author or her heirs.
Visit the U.S. Copyright Office website (see Resources). Under "Online Records," click on "Search the Catalogue."
Type in the title of the book you want to search for. This will generate a list of every book that has had this title, the owner/copyright holder, the registration number and the date of registration. Take note that some books copyrighted before 1978 may require a more extensive search either through the Library of Congress (if you live in the Washington, D.C., area) or through major city libraries that would have copyright records on microfilm. If you're unable to find the information you need from your online search, proceed to Step 4.
Write to the publishing company that originally published the book. In most cases, its address will be listed on the same page as the copyright notice and date. If it's not, you can either do a search in resource books such as "Writer's Market" (published annually by Writers Digest Books) or plug the name into your search engine. If the publishing house is still in business (or was absorbed by a larger entity), direct your request for information to the managing editor. This request should be in writing, not email, and include a self-addressed, stamped envelope for reply. If the publishing house is one that is now defunct, proceed to Step 5.
Conduct an Internet search for the author. For instance, you can put the author's name into a search at Amazon.com and see if he has written anything else for a different publisher. If he has, your next step would be to write to that publisher and query how you might be put in touch with the author or---in the event the author is now deceased---his family. In most cases, you'll be advised to send your correspondence to the publisher who will then forward it on to the author. Don't be put off by this; it's a fairly common practice to keep crazed fans from finding out where someone lives. Another approach is to make note of whether the author mentioned his literary agent in a dedication; instead of writing to the publisher, you then have the option of writing to the agent and making an inquiry.
Exercise patience and politeness throughout this endeavor, and always remember to thank people for their time. Should the material be available for you to acquire a new copyright, the next step is to return to the U.S. Copyright Office website.
Click the "Home" tab on the records page of the U.S. Copyright Office website you previously accessed in Step 2. There you will find the instructions for making application online or via snail mail. In either case, you're going to have to provide a complete copy of the material you're copyrighting. If you want to submit the material electronically, this means that you'll have to have the book scanned to a .pdf file for uploading. If you're going to submit everything by mail, you'll need to have the entire book photocopied. Partials are not accepted in either case.
Pay the required registration fees. When you receive the copyright documentation, be sure to file it in a safe place.