Find the copyright page, and it's usually on the reverse side of the title page. It will contain other information, including the book's publisher, acknowledgments and its ISBN.
Look for the original publication date of the book. There may be two dates, a copyright date and a date called the "first published" date. If the book was published in another country, there may be that date as well. A book with no date is probably a later edition.
Locate any information on the edition. Sometimes the publisher clearly prints this information. Other terms--such as "Reprinted," "Third Impression" and "Third Edition"--clearly indicate a reprint. If the book says "First Edition," other information on the page should corroborate that it is a first.
Decode the row of numbers, called the number line, on the bottom of the copyright page. The line of numbers goes from 10 to 1. The book printing is the lowest number in the series. With few exceptions, a number "1" in the number line indicates the book is a first printing. A number line "10 9 8 7 6 5 4 3 2 1" would mean a first printing, if the copyright page also says "First Edition," the book is probably a first. A row of numbers reading "10 9 8 7 6 5 4 3" would mean that the book is the third printing of the first edition.
Look for clues on the dust jacket. Reviews and title lists give the book away as a later edition. Check to see if the book is a Book Club Edition, which are printed for special groups and often mislabeled as "first editions."
Consult the author's bibliography for date and publication information, comparing it to your book. Research the binding, cover design and typeface of first editions. Images may be available online.
Show your suspected first edition volume to a book dealer for a professional opinion and valuation. Don't be afraid to get a second or third opinion. Research online, with auction sites and online brokers. The value of a first edition is determined by rarity, author signature, condition and market demand.