I've discovered that rats/mice are living in my home. At night they come into my study and chew any books they can find, so I had planned to exterminate them by placing rat poison in the study. However, I'm worried that they could eat it and die in my study somewhere that I can't find them. What are the steps to take or alternative extermination methods?
From a book protection, and not extermination standpoint, you could always build shelving that had doors on it -- like the ones used in law libraries, where a door drops down from the top to close things up.
(typically, they're glass or other clear doors, so you can see what's in there easily.)
I would think the mice/rats are not chewing on the books as a source of food (unless they really want lots of fiber in their diets), rather they are most likely gathering nesting material. As such, you may be able to prevent them from chewing your books by providing them another source of nesting material.
Try placing a few rolls of toilet tissue on the book shelf, and see if the rodents prefer that over the books. If that doesn't work you might also try some other materials, like cardboard, or other paper products like spare printer paper.
Ultimately the solution here is to eliminate the pest problem, there are some good suggestions on how to do that in this question "Theres a mouse in my house".