Open up the book and look through the first few pages, paying special attention to the left-hand side of the book. Publishers usually list the printing date on the inside cover.
Look at the title page to see if you can find a date. On some books, usually newer ones, you can find a printing date right underneath the title.
Flip through the book to see if you can find a date listed anywhere inside the book, especially printed on the bottom of the pages. In older editions of books, the publishers sometimes listed a date on the bottom of the book page.
Read the inside of the dust jacket if the book has one on its cover. The dust jacket sometimes includes the printing date.
Search online for pictures of the book. You may find it helpful to look for books by that particular author. There are websites devoted to specific authors where the owners include images of all the copies of the book, along with their printing date.