Enroll in a local dance instruction course that teaches the specific dance style you are interested in learning. Samba, swing, tango and waltz are just a few of the courses available in virtually every city in the U.S. Realize that everyone is in these courses to learn and that all of you will look a little silly at first. Relax and let yourself laugh at your mistakes instead of shutting down.
Practice your dance steps at home, alone. Put on a CD, get in front of your mirror and rehearse your steps and body movements until they are natural and graceful. Build confidence in private so that you do not need to be shy about strutting your stuff when dancing in public.
Choose dance partners that are more advanced than yourself; their skills will make you look like a pro, even while you are still learning. Trade dance partners frequently so you don't pick up bad habits or get into a rut.
Stick to the basics of any particular dance until you have mastered the beginner's level. Do not worry about learning more complicated dance moves until all shyness has disappeared; you will look better doing a few moves correctly on the dance floor than you will look fumbling more complex maneuvers.