The borrowing of books not contained in your public library is through
a system called Inter-Library Loan (ILL). At this point, unfortunately,
not all libraries participate in the ILL, so be sure to check with your
reference librarian first.
In the U.S., libraries participate in the OCLC (On Line Computer
Library Center) which uses the Online Union Catalog (OLUC)--a huge
(and I mean huge) database that lists which libraries have which
books. Member libraries (the OCLC charges a fee for participation) can
use the OLUC to locate books requested by patrons, then arrange to
borrow the book from the lending library.
Some libraries will allow patrons to use the Union Catalog themselves
to conduct searches, others will limit use to library staff. Regardless,
it is helpful if you can locate a book you want, and be able to tell
the librarian at least one library which has the book!
Note: if you live near a large city or county library, you may be
able to view a series of volumes titled National Union Catalog (NUC).
The NUC was the precursor to the OLUC, and is no longer being printed.
However, they do catalog books for various (U.S. only) libraries
with holdings into the last century.
If the OLUC is available to librarians, why do you need to go to
the time and bother of tracking down books yourself? The OLUC charges
libraries for access by the minute. Some libraries will conduct a
search for you, but may pass along the charge. Others will absorb
the charge themselves; money which could be better spent purchasing
books! And some libraries will not conduct a search for you using
OLUC due to prohibitive costs.