Type the name of the song into a free online music program like YouTube, GrooveShark or Spotify. The search results will bring up the names of any artists that have recorded the song. Listen to the various versions and see which one is by the right artist.
Insert the title on a free online lyric database like lyrics.com. For example, enter a lyric, phrase or the song title in the top search bar. In this case, type in "High Hopes" then click "Search." The site will display a list of artists who have songs titled "High Hopes." The top one in March of 2011 was Pink Floyd.
Use a music recognition program like Shazam. Open the program, click the "Shazam" button and point the microphone of the device Shazam is on to the source of the music. Play the song. Shazam will cross-reference the sound against its database and display the artist and title. Shazam can be downloaded from its main website.