Start learning part by part. Do not attempt to learn all the aspects of hula dancing at once. Hula dancing incorporates both hip movement and arms. The hips do the dancing and the arms do the story telling. Every song has a story so learn the hand motions to the story, and then add the hips to it. Learning in parts will make it a much easier process.
Watch videos online. There are many videos on YouTube that all exhibit how to dance to many different songs and tell the stories. They are instructional in nature and short, so watch them a few different times and learn how to do the dance. Videos are key because they demonstrate the proper way to do the dances.
Once the child has learned the dance, practice in front of the mirror. Sometimes he may think that he is doing the dance correctly, but seeing his reflection while he dances helps him be able to fine-tune the dance. If he is using a laptop, put the laptop near the mirror so he can watch the dance and himself.
Have the child study techniques so that she can fully master the beginning principles of hula dancing. If she masters the basics, picking up on new dances will be much easier and go faster. As the child becomes more advanced in her hula techniques, she can learn other songs. Songs become more and more intricate, so make sure to find very detailed instructions so that she can properly execute them.