Explained as well as I can.
Visit him and talk with him to start borrowing books.
The basic principle is that the first time you speak with him he will let you borrow 1 book.
Once you've walked around enough different rooms and areas in the castle, and talk to him again, he will let you borrow another, for total of 2 books.
And same again for walking around more different rooms and areas, for a total of 3.
Note: You can get all 3 book allowance before fighting Andrealphus.
Except that this bugs quite a lot, you will usually get at least 2 books, but I've had games where I've been stuck with 1. From my experience fighting bosses seems to have a negative effect on getting more books from him.
NewGame+ will always force set the number to 2, first time you talk with OD will show 0/2 books. And you won't be able to get more or less.
You unlock more books that you can borrow with Map%.