You need as many tables as required to store the necessary data. How many tables that ends up being is going to depend on your design criteria.
As you said, you'll need a table to keep track of students, and one to keep track of books. You'll also need a table to keep track of check-outs (and depending on how you set it up, a table to keep track of which student record is associated with which check-out).
You could further break things down and add a table for authors containing additional info about the authors themselves. You could have a table of metadata that extends the books table. You could have a table for reserved books (so that if a book is checked out, a student can reserve it).
Your question is entirely subjective. It depends on how complex or simple you want to make the system.
Technically speaking, you could do it all in one table if you wanted to. It wouldn't be very efficient or flexible, and god help you if you ever needed to add new features, but it would technically work.
Likewise, you could do it with 5 tables or 10 tables or 50 tables, depending on your design.