This is a little difficult.  The most important thing to remember with MLA citing, is that it is simple and typically follows common sense, but it always gives credit where credit is due.  If the book you are using is of significant length (ie: not a short story), and it is clear from your review exactly what title and author your are quoting, do not worry about putting the author's last name in the parenthetical citation.  It would likely seem redundant.  However, if you are directly quoting text, you will need to cite a page number, if the quote is from a work of significant length.  If it is a short story, you might cite a paragraph number.  If it were a short poem, you would cite a line number.

Of course, if you are required to do MLA, you are also then required to do a works cited.  Be sure the entry in your works cited is the exact edition you are using for the page number citations.  With any other works referenced in your review, do not change anything (no italics) in the formatting.  Just reference the same way you did the actual book.  Be sure to give credit to the author you are citing, either in the sentence (ie: "According to Roger Smith...") or at the end with last name and page number in parenthetical citation.