I have a business license. Permits were not required where I live. I can use public parks, sidewalks, streets.
Check with your county/town.
I use a small park in my town. I am aware and respectful of the people living nearby.
I started 4 years ago with 17 and today have 30/there are two trainers.
Read through the questions on this site, you will find a lot of great ideas
I agree with Sue. You should check with your city if you need to get any permits in order to use their parks/spaces as your first step. Beyond that the possibilities and opportunities are limitless. You can do a newsletter to your current clients, do a press release to your community, contact the park district and see if you can partner up with them and advertise your class through their website, put flyers out at different places (coffee shops and athletic stores are great for this), ask someone you know and wants to take your class to help you organize a class for you (inviting friends, family, etc.) and give them free sessions in return. There are so many ways you can do this that no one way is better than others. Don’t forget to get liability insurance before you start any of your classes. The Park Districts will also require for you to have one as well. I wish you good luck.