Dancing can be a lot of fun and be great exercise, too -- both for physical health and mental discipline. A particular quirk of dance classes, though, is that you need shoes that will allow you to glide across the floor, which is quite different from activities like running and basketball, in which shoes that grip the ground or court surface are essential. However, that gliding ability can sometimes be too apparent, leading to you slipping and falling. For that reason, if you're about to take up dance, you'll need to have a set of strategies for making those slippery soles a lot "stickier."
Smooth Movement, Less Injury
First, you need to understand why the soles of your dance shoes have to be smooth. When you dance, you need to turn and slide and do all sorts of movements that have the potential to twist your ankles if your feet don't move with the rest of your body. Because the main literal sticking point is where your shoes meet the floor, you need both sides of that connection to slip past each other easily. This is why so many dance shoes now have faux-suede soles; that material is nice and smooth without being scratchy to floors.
Too Smooth Movement, More Injury
But if the soles become too smooth, such as old faux-suede that is tamped down into a slick surface over months and years, or the satiny cloth of ballet slippers, then the slipping can become literal. Your feet can slip out from under you, leading to more injury. So, you need to reintroduce a little bit of friction that's just enough to stop the shoe from going every which way it wants to, regardless of where you need it to go.
Rosin, Brushing, and Water
Three strategies help. One is powdered rosin, that stuff that looks like chalk. Dance studios often have a box of it that you step in, and you can buy your own granules, too. Another is, if you have faux-suede soles, to brush the soles regularly to ensure the material doesn't pack down into a slippery layer. The third is wetting the sole lightly, which doesn't last long but works well for a short routine or warm-up.
The dance studio owner and instructors will have their preferences and policies regarding rosin and water, so double-check with them before you begin your class. Brushing you can do every few days on your own.