Check the record, tape or CD liner if you have the CD that the song appears on. Many times, the back side of the liner has the recording date in relatively small print.
Go to the band's website and look for a "discography" or "music" section. Find the CD that contains the song you're looking for. If you're not sure which CD has the song on it, click on the various CDs on the site. Most bands list the CDs they've released along with the individual songs on them and the year of release.
Use a common search engine to search for the song's title. Some of the results should list the date of release.
Search for the song title or artist in a specific database for music, such as http://www.song-database.com.