Contact the publication or place where you saw the image. They can tell you the name of the photographer who took the image, or they may own the copyright themselves.
Find the name of the photographer. Most photographers hold the copyright to their images even after their publication. If you can determine the photographer, you can contact them to determine who owns the image and obtain rights to use it.
Find the person who holds the copyright. If the photographer no longer holds the copyright, they can point you to the person or company that does. Many photographs have a shared ownership, meaning that the photographer and an individual, company or series of both have equal rights to use the image.
Contact the Library of Congress to identify the owner of the copyright. This method can take months, but if other methods fail, it may provide you with a definitive statement of who holds the photo's copyright.
Contact the person or business that owns the copyright on the photo. Tell them that you wish to obtain the rights to use the image for publication in a book. They will tell you if you may use the image and the cost and restrictions for its use.
Draft and sign a contract with the owner of the copyright. This contract should explicitly state what you may use the image for and how much money you will pay the copyright owner. Many photographers and publishers have standard contracts for use of their images, but you may wish to consult a lawyer either on your own or retained by your publisher to draw up a contract on your behalf.