Look on the book's copyright page to find out the most important information. This page is the one with smaller print and contains information about the publisher. Most of the time it will say something like "Copyright 2009 by ABC Publishing."
Search for a line of numbers or letters on the copyright page. The first number or letter in the series is likely the printing run for the book. For instance, if the line reads "1 2 3 4 5," then your book would be the first printing in this edition. If it reads "B C D E F," your book is a second printing.
Rely on the printing numbers more than any statement about edition. Many books will say "First United States Edition," but there may be many printings in an edition, and the first printing is almost always the most valuable one.
Check the size of the book compared with other books on the shelf around it. This is useful if you are scouting for books in a used-book setting. If the book in question is smaller than the books around it, there's a good chance you have a book club edition. No matter what printing you have for a book club book, it will have almost no value except in very rare circumstances.
Look on the front flap inside the front cover. The front flap of the dust jacket should have a price in the upper right-hand corner. If there is no price, the book is probably a book club edition.
Many publishers have their own unique way of indicating first printings. For instance, after 1980 Viking Press added a number row only to second printings or later. So a first-printing Stephen King from Viking, for example, would not have a number row. Research individual publishers if you are collecting certain valuable authors or books.