To find out information about people (composers, performers, etc.), places, and concepts related to music, start with Grove Music Online in Oxford Music Online. It's the most important scholarly music encyclopedia. This online resource is updated regularly.
Once you find the article in Grove Music Online about a composer, scroll down under Article contents to the Works link to find a list of all the composer's compositions.
Works by Beethoven are identified in the left-hand column by opus and WOO (Werk ohne Opuszahl, "work without opus") numbers. His works published in GA are identified by the volume in which they appear (roman numeral) and the position in the publisher’s continuous numeration (arabic number). His works published in NA are identified by category (roman numeral) and volume within each category (arabic number). The works lists for less prolific composers aren't presented in tables, but the organizational principles are the same.
Then perform an ALL FIELDS (Keyword) search of the composer's complete works in the library catalog to find its call number; for example, "Beethoven neue ausgabe samtlicher werke"