Unfortunately, the rules to identify 1st editions are not always easy to define because the conventions vary from publisher to publisher. However, there are some typical criteria to look for. First of all, the information is contained on the copyright page. Knowledgable eBay sellers of collectors books will often provide a clear photo of the copyright page. If not, you may ask them to email you a clear digital photo of the page, or ask them to post it on the listing, especially if you intend to pay a considerable amount for the book.
The most common identifier of a first edition are the words "First Edition", "First Printing", "First Published" or "First Impression" on the copyright page.
Sometimes there will only be a line of numbers at the bottom of the copyright page to indicate that the book is a First Edition/First Print Run. This will be a series of numbers in consecutive order such as:
9 8 7 6 5 4 3 2 1
Some publishers, such as Random House or Bloomburys (publisher of Harry Potter books) will drop the words "First Edition" after the first print run, and although it is still a first edition, subsequent print runs will have a series of numbers on the bottom, such as above. However, the lowest number in the sequence will indicate the print run. For example:
10 9 8 7 6 5 4 3 2
Print runs are often important to collectors and even if the book is not a First Edition/First Print Run - it may still be valuable. Print runs are identified on the copyright page as indicated above. For example:
10 9 8 7 6 5 4 - indicates a First Edition, 4th Print Run
Generally, if the lowest number of the series is '1', then this is a first edition, first print run. If the lowest number is 2, then this represents a first edition. 2nd print run, and so forth.
An example of a Harry Potter 1st Edition, 2nd Print Run book.
These are only general guidelines and as previously discussed, conventions will vary from publisher to publisher. Good reference guides include "Pocket Guide to the Identification of First Editions" by Bill McBride; "ABC for Book Collectors" by John Carter; or "Modern Book Collecting " by Robert A Wilson.
Information obtained from Empty Mirror Books on the internet include excellent references, and also source material for this Guide.