Do a little research on the history of swing dancing. Remember the children are inquisitive and will be more interested the more information you have about swing dance.
Watch other individuals perform swing dance. Go to a dance club with your partner or a friend and watch social swing dancing to get a feel for the vibrancy and different forms of the dance.
Take a basic swing dancing class yourself before attempting to teach the child to swing. Learn basic steps and safety precautions so that you can ensure both your safety and the child when teaching them the steps.
Sit down with the child and pick some music that they would like to learn to swing to. Clear a large area so you and the child can have freedom to dance and be free of obstructions that could cause harm.
Show the child what you've learned or even watch a tape of some swing dancers to get the child interested in swing dancing. Let the child experiment and guide them; let them experiment with their own way of doing the moves and be less directive.