It's called "checking out a book" or you could use the term "borrowing."

Look, this "it's not stealing" argument is a bunch of hog wash. If you think it isn't stealing because the "stolen" goods are simply a copy, why do you use the term "piracy"? Did pirates make a copy of the loot?

When you say someone is stealing music -- everyone knows what is happening. People use the same term with cable television -- they're stealing cable. It means they are enjoying the benefits of cable -- without paying the cable company.

You can use whatever term you want for the behavior -- we all know what it is and why it isn't right and it is just as wrong as stealing IMO.