Take voice lessons, and practice relentlessly. Develop and improve your vocal instrument.
Become skilled at sight singing. A backup vocalist knows how to read music.
Vary your style. If you mostly sing country, make sure you can also sing R&B, jazz, and other styles of music. Be versatile. This way you will have work more.
Develop pitch. It is important to be able to change your voice depending on who you are singing with. Singing background for Patti LaBelle would be very different than singing for Kelly Clarkson.
Show your desire to get along with those you work with. No one wants to work with someone who is difficult.
Record a demo CD. This CD should include a compilation of several styles of music. Include solos as well as you singing in a group. The tape demo should be no longer than four minutes.
Attend AFTRA (American Federation of Television and Radio Artists) and SAG (Screen Actors Guild) singers meetings to learn about jobs.
Publicize yourself. Go places where they need music and ask for work. Place an ad in the Service Directory and in the classifieds of the newspaper. Invite potential employers to places where you will be performing.