As a group fitness instructor, do my clients make payments to me OR do I need to set up a business license/account?

After owning two companies, I will advise you to create an LLC and then operate under that company. Yes, it will take some effort to do it and very little capital. If you can consult a lawyer or an accountant that would be the best way to go about it. You will also be able to expense all of your expenses associated with running a business (including mileage, gas, clothes, certification fees, liability insurance, etc.).