Library editions can be cleaned much easier than regular editions, since the bindings can more easily withstand exposure to moisture. I decided to use some library editions that I just acquired as an example.
These books were absolutely filthy. They felt grimy when I removed them from the package, and the books have a musty odor. The text blocks are quite foxed, and I suspect that the books were kept in some type of outbuilding by their general appearance.
I knew that these books would not clean up very well, since the dirt looked to be embedded in the covers. However, I wanted the books not to feel nasty, so they were still worth cleaning.
Soap and water would probably work just fine, but years ago, I purchased some Demco book cleaner, which is what I use.
I have to be very careful with the printed parts of the covers. The print tends to come off of library editions fairly easily, so those parts cannot be cleaned as well. I first start with the unprinted areas where I know that I can rub very hard. Last, I go over the printed areas with a much lighter stroke and for a short amount of time. I wipe each area dry before I go to another part of the cover. Last, I take a dry cloth and buff the cover back as shiny as I can get it.
This is what the books looked like after my first attempt.
I thought I could do a little better, so I tried again with the following result.
I could probably get a little more dirt off, but I decided to quit. As stated, I knew that the books would not clean well, and I will not be able to get all of the dirt off no matter how long I try. If I were to go much further, I would end up taking off too much of the print.
These library editions were not the best examples since I could not clean them well. I have had filthy library editions clean up quite nicely, to the point that the books ended up a completely different color in the end. In those cases, the cleaning process is very satisfactory.