Open the book to the title page. Look for a copyright or reprint date. This will tell you exactly how old the book is. Some books have several editions, so the reprint date is a big clue.
Turn the book over to the back cover. Look for the copyright date for the book or the cover art. Usually, you can infer that the book was made not long after the cover was copyrighted.
Look up the publisher online. You may discover the print date on the publisher's website.
Research the author online. His bibliography may list the print date of a particular book. You might also find that information on his website. You can also submit the book title for a general online search.
Take your book to a fellow collector. A more serious collector can use some of the state-of-the-art techniques to determine the book's age.