I'm not sure how regular people encourage others to dance but I have a great friend who is really outgoing and her birthday is only a couple weeks before mine so we both had the same first stake dance. I was standing with my older brother by a wall busy being totally worried about what people would think if I went and danced with the other 10 people out there when she ran up grabbed my hand gave me a hug screamed my name at me and pulled me into the "dance floor" Now that in and of itself isn't exactly normal but the weirder part is we barely knew each other at the time. She's just amazing with names and remembered me from girls camp. Ever since then I'm pretty sure more people dance we've convinced a lot of people that being a wall flower, pretty a flower as you may be, is just boring and unless you have some reason to sit/stand on the sidelines you might as well join the people having fun in the middle.
I know this isn't a be-all end-all solution but it sort of goes to show that if you encourage people they can be convinced. I used to be pretty shy but now I'm usually one of the first people dancing.