I am a Bharata Natyam(Indian classical) dancer and I am on H4.
I would like to start my own dance classes.
What kind of Visa can I apply for and how to go about doing that?

You should consider investor visa, but one of the conditions is you need to invest $500,000 as business partner ot $1,000,000 as a sole propriety. The good thing is there is no quota on this category but there are some legal issues you might want to consult immigration attorney before making any decision.

Well, I'm going to assume you don't have a million dollars here... apply to USCIS to get another visa, like an H1-B which I assume your spouse has.