Call the radio station. Look up the number in the advertising section of the phone book and use the request line or studio line. Ask the DJ the name of the song that was played at the time you heard it. You’ll have to call quickly, because nobody’s going to remember an hour later what song was played at a certain time. They're also probably not going to search through a previous playlist.
Check the radio station’s website. Many stations carry the day’s playlist on their site, and you'll be able to identify the song if you know what time it was played. If the playlist is not there, email the station if you feel uncomfortable about calling, and ask if the DJ would be kind enough to send you the name of the song and the band. Add a sentence thanking the DJ for helping.
Check a playlist service website that links to the playlists of many radio stations nationwide. See Resources below for an example.
Keep some of the lyrics in mind until you can get to a computer and do a search, if Steps 1 and 2 aren't feasible. Remember some unique lines from the song, rather than very common lyrics. “Yeah I love you baby,” for instance, is going to get way too many hits when you do your search. Type a line or two that you remember into a search engine text box along with the word "lyrics."