If you are looking for reviews that came out when the book was published, you will probably need to consult a print source if the book was published prior to about 1990. If you don't find anything in the volume for the year the book was published, look in the surrounding years (for example, the prior year and/or the next two years).
Book Review Digest (1905 - 2013): Index Area, Basement Compact Shelving: Z 1219.C96: "Contains citations and brief excerpts of reviews of juvenile and adult fiction and nonfiction published in the English language. The reviews originate in a group of selected periodicals in the humanities, social sciences, and general science published in the U.S., Canada and Britain".~prefatory note
Book Review Index: (1965 - present): Index Area, Basement Compact Shelving: Z1035.A1B6 Contains citations to reviews of books, audiobooks and e-books. Reviews are from "over 400 publications from the U.S., Canada, Europe and Australia, [and may provide] critical comment, a description of the book's contents, or a recommendation regarding the type of library for which a book is suited". ~introduction
Reader's Guide to Periodical Literature: (1900 - 2012): Index Area, Basement Compact Shelving: AI3.R48: A cumulative author-subject index to English language periodicals of general interest. The main part contains citations to articles, organized by author and subject, arranged alphabetically. Beginning in March 1977, volume 36, a section of Book Review citations, arranged alphabetically by the author of the book being reviewed, is at the end of each volume.
Readers' Guide to Periodical Literature Database (citations back to 1983, full-text from 1994 - present).
New York Times Index (1851-present): Index Area, Basement Compact Shelving: AI21.N44. Subject index for the New York Times. Book reviews are found under "Books--Reviews" unless many books were written on a particular subject at that time, then reviews may also be found under the heading for that topic. Consult "How to Use the Index" at the front of each volume to understand how to read the notation. The actual article will be found in the New York Times on microfilm, located near the periodicals area on the main floor.
In Academic Search Premier, search for the author AND book review, such as faulkner AND book review. In Project Muse, check the box for Reviews on the left side of the page.