The names of songs from movies can be found on the Internet Movie Database by searching the movie title and scrolling down to the soundtrack section. There is usually one song listed and an option to click a link to see more, which will list the entire soundtrack.
The soundtrack information found on IMDb lists the name of the song, writer, performer and, often, the label that produced the song. This list usually contains both instrumental and vocal tracks from the movie.
Soundtrack.net is another source for finding names of songs from movies. Movie titles are listed alphabetically. Once a movie title is selected, the information about the soundtrack will appear, then clicking on the movie title again will give a list of the individual songs from the movie.