Call the radio station. You might not get to talk to the actual DJ that played it, but the assistant or intern answering the phones should have a playlist and be able to tell you the song title, artist and the album.
Research the singer. If the song title escapes you but you recognize the singer or band, use that information to help you find the song title. Look for the band's official website or check out fan club sites; most of these official sites will list discographies with song titles and lyrics.
Visit a music store. The employees at your local music and electronics store have to be knowledgeable about new songs and music for their job, so they might be able to help you find the title to your mystery song. It will help if you know the band or at least part of the lyrics, but if you ask around enough you're bound to find a music buff that knows exactly what you're looking for.
Try a search engine. Lots of online music search engines let you look for artists, lyrics and song titles as long as you know some information about the song. If you don't know the title or singer and just have a snippet of the lyrics, these wide-range search engines can still help (see Resources below).
Ask a know-it-all. We all have those friends that know every song on the radio and every new hit that's out there. If none of your other resources work, ask your friends. If you have different musical taste than your friends and family, try an online forum dedicated to the genre of music. A fellow fan that you meet online might know the song you're looking for and be able to help you out with the title.