Learn Harmony

To sing harmony, you have to learn harmony as a part in the sheet music.  Learning harmony is a process that many people have mastered and you can, too.  Once you master singing harmony with the sheet music, you can learn to sing harmony by ear.  This is a harder thing for some people and easier for others. 

To learn harmony by ear, just listen to the people singing around you.  Listen to the radio and try and sing with the backup singers.  Copy what they're doing.  You may have to turn the music up loud to be able to hear the harmony clearly, and still hear it while you sing, but that's more fun, isn't it?

To really know if you're doing well singing by ear, you can try singing harmony to solo music.  Some songs only have one singer and they're called solos. If you are doing really well, you will be able to make up a harmony part that sounds good with the singer who's singing solo.  (Of course, once you start singing, it is no longer a solo, but a duet, right?)

Keep in mind that it can take time to learn harmony, especially to learn to sing it by ear.  Be patient with your efforts and keep practicing with lots of people and different types of music.