A used bookstore where I live sells little paperback-sized covers made of something like leather. You could also make one similar to the kind hardcover books have out of stiff paper.
It's not hard to keep them clean if you keep them arranged on a shelf, don't read them while you're doing something messy, and dust them every once in a while. If you have to carry one around with you, put it in a separate bag or container from anything else you have with you. But you shouldn't have to worry too much - I don't do anything special with my books and the worst that happens to them is that their spines get a little bent after I read them a few times.
