Practice proper singing techniques. This includes using good posture, relaxing your jaw and maintaining steady breath control as you sing.
Learn the melody line of song well. The melody is the part that the lead singer performs. You have to know this well before you can add background parts to it.
Add harmony notes to the melody. Harmony notes blend with the melody notes. You can sing harmony notes by reading the actual music notes on a sheet of music, or you can listen for which notes blend with what is being sung.
Sing your part at a slightly lower volume than the lead part. The background vocal should support and not overshadow the lead.
Intersperse your singing throughout the song. Most songs sound best when the background vocals are present only at certain points for emphasis and not for the entire song.
Practice. It may sound overly simple, but the more you try singing background vocals, the more you will develop your talent.