Start with a single dance. There are numerous dances that fall under ballroom dancing, such as the waltz, the cha-cha and swing dancing. However, it is best to start with a single dance or style in the beginning, and stick with it until you are comfortable.
Attend a dance class for the style you wish to learn or watch an instructional video. Bring your child with you, so he is exposed to the basic mechanics early, even if he is not yet actively participating. Ideally, you can use your child as your dance partner, depending on his age.
Practice the basic steps of the dance in front of a mirror, so you can watch yourself and correct mistakes.
Involve your child more in the dance, as you get more comfortable. You will be better able to instruct her, once you are familiar with the movements yourself. In addition, teaching and reviewing the dance steps with her, will help solidify them for yourself.
Partner your child with another kid the same age who is also studying dance, so you or an instructor can watch them and critique, since it will be easier for your child to get the specifics down when dancing with someone his own size. This is also a good social exercise for him.
Repeat the steps daily, until your child is comfortable with them. Then move on to another dance, if your child is enjoying the experience.