If you're in the US, you can contact your state's regulatory board. There's a specific license needed in Tennessee, for example. Tennessee has a TN Department of Commerce and Insurance that controls the licensing in the state. See link for example... http://www.state.tn.us/commerce/boards/i…
You might also have a city and county requirement for not just starting a beauty salon but starting any business. You might also want to check with your county clerk's office.
I dont know where you are writing from, but as of two years ago in British Columbia Canada you no longer need a licence to do hair any more. Shocking but true! So here one would only need a business licence.