I have been a bookseller for over ten years, and buy a lot of books at tag sales and library book sales. Many of these books have have soiled dust jackets and/or covers. After much practice, I have my technique boiled down to the bare minimum of effort that gives the best result.
Dirty dust jackets. In my early days as a bookseller, I used to use a cleaner such as ’409′ or one of the other gentle cleaners. But even these ‘gentle’ cleaners have chemicals in them that may harm the book and its dust jacket over time.
I now have two things I use to clean books and dust jackets. Water and Ronsonol lighter fluid. BUT, I do not use water on any hardcover book with cloth-covered boards or on a plain paper dust jacket (more common in the early to mid-20th century) . They just absorb the water. Also, the cloth covering some books published in the early 1900′s have some kind of filler that turns to a sticky glue when dampened. Wipe these types of books off with a clean, dry soft cloth.
To be able to clean a dust jacket, it has to be the kind with a shiny coating. Hardcover books and paperbacks with shiny covers may be cleaned the same way as a shiny dust jacket.
I have found that it is easiest to clean the outside of a dust jacket when it is still on the book. When cleaning the inside, remove it and lay on a flat surface to help prevent wrinkles and tears.
Do not use water on a dull, plain paper dust jacket or on the inside of any dust jacket – the surfaces are not coated with any water-resistant finish. If it is dusty or soiled, it is better to clean it gently with a clean, dry soft cloth and leave it at that.
For the coated (shiny) dust jacket, just dampen a soft cloth with plain water and gently wipe off the soiling. Immediately, wipe dry with a different soft absorbent cloth.
If there is some soiling that will not come off with water, try dampening a corner of a different cloth with lighter fluid and rub gently.
If you still have a soiled book and/or dust jacket, and the book is valuable to you in some way, a professional bookbinder or paper conservator may be able to restore it. Be careful when making this decision. Depending upon the book in question, it’s market value can be affected for better or worse. Usually, such books are better off when left in their original condition.