Some strategies you can try are:
Contact the publisher and/or author directly.
While it does not give total sales figures and represents only one retailer (though a large one), the record for each book on Amazon.com includes information on its ranking in sales compared to other books offered by Amazon.
In some cases of famous authors, researchers may have already determined this information. Check biographies of the author and bibliographies of works about him or her.
Books that identify first editions for the rare/used book trade, such as FIRST PRINTINGS OF AMERICAN AUTHORS (Wilson Quarto PS88 .F57x 1977), may contain this information.
For books from 2001 to the current date, approximate sales data may have been gathered by Nielsen Book Scan, a subscription service marketed mostly to publishers and bookstore chains; however, the University of Minnesota does not subscribe to this service.
For bestsellers, PUBLISHERS' WEEKLY (Wilson Periodicals Room) includes estimates of total sales in annual bestsellers lists, which are usually printed in March for the previous year; for example, the 2001 lists are in the March 18, 2002 issue. BOWKER ANNUAL: LIBRARY AND BOOK TRADE ALMANAC (Several locations including Wilson Reference Z731 .A47) also includes this data.
Rarely, you might find an individual news story about the book in PUBLISHER'S WEEKLY that gives such figures, especially if it is an unexpected success.
Check the copyright page (usually the reverse of the title page) of the most recent edition of the book you can find to see if it has gone into multiple printings, and if so, how many. While this does not provide real figures (since the size of each printing is rarely specified) you can assume that a title that has gone back to press several times has sold well.