The easiest way to find song titles by artists is by using a normal or musical search engine. As you search, you must give the search engine some core identifiable part or piece of the song, usually the lyrics, so that you get the correct results.
Another tip to help you find song titles by artists involves searching the song's lyrics in a database like WhoDoesThatSong.com. There are more databases with collections of songs organized by artists names and song titles which makes searching easy as long as you know a piece of the song.
Some applications also allow users to search the lyrics of a song as it plays. The results often give further details about the song like its title, the artist's name and year of release. Additionally, there are social sites like WatZatSong.com where members help each other to get song details where only a piece of the song is known.