Really want to dig into your composer's life and times? Get familiar with the "M" section of the Library.
On the 4th floor, find the call numbers starting with M.
The Library of Congress classification system divides out music books the following ways:
M= musical scores
ML= music literature
MT= music technique, music education, and music appreciation
If you know what book you're looking for, and its call number, always be sure and check around that book to see if there are others that you might also find relevant to your research.
Finding biographical information on your composer should be fairly straightforward, unless you've selected someone particularly obscure.
After you've consulted The Grove Dictionary of Music I recommend the following online sources: