Determine the main genre of the music: vocal or instrumental? For vocal music (i.e., music with singing), continue to Step 2; for instrumental music (i.e., music without singing), continue to Step 4.
Listen to the beginning of a vocal piece and note its first line. This will almost always be the title of a piece, if not the only title by which it is known. (For example, the piece "Sous le dôme épais" from Léo Delibes' opera "Lakmé" is commonly known as the "Flower Duet.") Since the first line of pieces in foreign languages may be difficult to parse, use your knowledge of the piece's composer and general contents to narrow your search.
Determine the titles of larger vocal pieces based on the titles of pieces within them. For example, once you determine that the title of two pieces in a larger work are "For unto us a child is born" and "And the glory of the Lord," you can search for recordings or sheet music of those titles to determine that they are from the oratorio "The Messiah" by George Frederic Handel.
Try to narrow the genre of instrumental pieces even further based on the instrumentation (e.g., solo piano or string quartet) or structure (e.g., sonata or fugue). Instrumental pieces are generally known by a work number (e.g., Symphony No. 9 by Beethoven) or key (e.g., Canon in D by Pachelbel), but may be known by a nickname (e.g., the "Surprise" Symphony by Haydn). Compare your recording (or memory of the music) with sheet music or other recordings that include the piece's title.
Consult someone familiar with classical music. Even if she cannot identify the piece for you, she may be able to help identify the composer, time period or type of work, narrowing down your search.