Learn the book's popularity. If the book is not a household name, then the sale records will be private, because most publishers do not want people seeing low readership numbers. In contrast, sale numbers for classic novels and bestsellers are usually promoted by publishers to boost sales even further. According to publisher Dan Poynter, in order to become a best seller, it takes 35,000 copies to be sold, while to make the top 10 on Amazon, author Brent Sampson says, at least 500 must be sold in one day alone.
Research the book in business articles. Chances are magazines and websites such as Forbes and Publisher's Weekly will have the revenue of a particular book if it is garnering headlines, as well as the source or publishing company that provided that information.
Look up the book on Nielson Bookscan. Bookscan is the only database that provides sales numbers for most books---even the less popular ones---down to the number figure. The drawbacks are that it costs $1,000 to get access to Nielson's system, and it provides statistics only from the major outlets.
Contact the author or publisher. If the specific book is by a well-known author, then the publisher will provide details of its sale history, or provide a service that will. If it is a lesser known author, try contacting the author through e-mail or phone, or visit his website.