How to Identify a First Edition
First, I can't actually tell you how to identify a first edition — at least not without writing a book, and even then I'd likely miss something. What I can do is tell you how to identify some books which are not first editions. There are clues you can look for.
Book Club Editions
Book club editions are, for the most part, not first editions — although there are a few cases, especially in science fiction, where the book club edition is the first hardcover edition.
Book-of-the-Month Club editions often have a mark on the back cover called a blind stamp. It might be in the form of a circle, a box, or a maple leaf, impressed into the cloth binding in the lower corner of the back board nearest the spine, under the dust jacket.
Be cautious of books with no price on the inside front flap of the dust jacket — this is often a sign of a book club edition. It is not a hard rule, though: many Canadian titles never had a price on the jacket, and the same is true of some university press and small press books.
Some book clubs include a statement on the inside front flap of the jacket: A selection of the Book-of-the-Month Club, or simply Book club edition. Another common indicator is a small rectangular box — usually white — on the back cover of the dust jacket, containing a series of five numbers.
Reprint Publishers
Some publishers specialised primarily in reprint editions. One of the best known is Grosset & Dunlap. Others include A.L. Burt, Avenel, Bison, Blakiston, Collier, Cupples & Leon, Goldsmith, Saalfield, Sun Dial, and Triangle. If you have a book from one of these publishers, check the copyright page to see whether the copyright matches. If the book was published by Grosset & Dunlap but the copyright page reads Copyright 1923 J.M. Dent, you almost certainly have a reprint.
Reprints by the Same Publisher
Identifying later printings by the original publisher is trickier. Sometimes it is obvious — the copyright page may state Reprinted 1982 or similar. Many publishers use a number line:
1 2 3 4 5 6 7 8 9
The lowest number present indicates the printing. If the number line reads 3 4 5 6 7 8 9, you likely have a third printing. Some publishers use a descending sequence — 9 8 7 6 5 4 3 2 1 — where again the lowest number present is the printing.
Unfortunately, publishers do not make this easy. Random House for example has used a number line that starts with 2. So if a Random House title states First Edition and the number line starts with 2, then it is a first. There are all sorts of other special cases and exceptions, and there simply is not room to list them all here. That is what the reference books below are for.