Dry cleaning (as covered in a previous post) will only remove surface dirt. More advanced cleaning techniques include taking the book apart and washing each page.
As you can imagine, that is a time consuming and costly process. I do not recommend you try this without some professional guidance on hand. For that reason I will not be covering the technique on this site. There are, however, many libraries and colleges that run single day workshops for you to learn and practice on your own books.
If simple dry cleaning does not seem to be successful, it may not be feasible to clean the book.