Locate the book. First editions are available online, but seeing and touching the book may help you get a sense of its value. Visit antiquarian book fairs and talk to book sellers.
Make sure the book has the Putnam logo, which is a black rectangular shape with these words inside it: "Putnam Est. 1838." The publisher's name can also be found on the title page of the book, along with the book's title and the author's name.
Check the copyright date, which will be found on the "verso" page, on the back side of the title page. The copyright date should be the same as the year the book was published. So, the Putnam first edition of "Lolita" should have a copyright of 1958.
Look for extra information on the copyright page. Putnam does not specifically indicate that a book is a first edition. However, it does indicate if it is a second or third edition, and so on. If nothing says otherwise, the assumption is that the book is a first edition.
Find the sequence of numbers on the copyright page. Putnam first editions tend to have a full number line, that reads "1 2 3 4 5 6 7 8 9 10." They may also have a number line reading 1 3 5 7 9 10 8 6 4 2.