There are no definitive answers or criteria for indicating whether a publication is a first edition or not. This can greatly vary from publisher to publisher as some publishers do not identify their first editions at all. However, there are some general guidelines one can use to identify a publication.
The common identifiers would include noting First Edition, First Printing, First Published, Published, or First Impression. These notations would appear on the copyright page. For a more definitive answer, I would recommend consulting the author, a bibliography, or the publisher as your best resources.
Publication Statements – typically, if a book is a first print, second print, or reprint the publisher will mention those terms on the copyright page as noted prior. However, this is not always the case for all publishers as some will reprint without making mention of the other editions or reprints. To avoid confusion, I would recommend contacting the publisher directly to confirm the status of the publication.
Publication Dates – The publication date is the date on which a publication is produced and offered to the public. In books this date is generally presented as a year and is found on the back of the title page. In journals this date is presented as day, month, and year or month and year and season. If the book shows no date, then it is most likely a later edition.
Useful resources to consult would be the Library of Congress online catalog http://catalog.loc.gov, the Bodleian Library http://www.ouls.ox.ac.uk/bodley, the Copac – The Union of Libraries http://copac.ac.uk, the British Library Public Catalogue http://blpc.bl.uk, WorldCat http://www.worldcat.org, or the Harvard Theatrum Catalogorum http://www.fas.harvard.edu/~earlymod/tc/europe.htm
Print Key – The printer’s key is typically referred to as the number line is a convention that publishers use to indicate the print run of a book. It is found on the copyright page. It is the sequence of numbers that varies between publishers. Typically, it is a series of numbers or letters in the following example 10 9 8 7 6 5 4 3 2 1 which is indication of first print or 10 9 8 7 6 5 4 3 2 which is indication of second print, etc. Occasionally a letter line is used such as a b c d e f g h i j k.
As a resource I would recommend obtaining a copy of “Bill McBride’s Pocket Guide to the Identification of First Editions”
Are first editions valuable?
Although all publications that are printed have a first edition, not all first editions are valuable. However, a first edition can have value if there is a demand for it and whether it is first edition or second edition does not matter in this case. Another factor to consider for publications that are in demand is condition. If a publication is in fine condition, then typically the value will be higher, but if a publication has flaws, it will be worth significant less. Collectors of books will tend to pay a higher premium for copies that are in excellent condition.