It varies a lot by town/city–so you really do need to check with your town’s zoning board. Sorry!
The problem with home based businesses is that neighbors object to traffic (cars parked). You didn’t say what your business is. If you are making a small product, say jewelry, then maybe you can get away without it being zoned, just don’t advertise your home address…get a business address from one of those Mailbox places. If you are merely making calls from home then just get a second phone number or an 800 number and work. What is it you plan to do? Some people set up their businesses in storage units (some storage unit places allow this). My mechanic used to have a storage unit place. Tell us just what kind of business you intend to do.