Is it legal to live and run a business out of a rental house that is zoned residential?

Each county has its own procedures for how to get a zoning "variance" -- that is, to carve out an exception to how an area or property is meant to be zoned.

Just getting signatures from your neighbors (and your landlord) may not be sufficient, as the county may also need to consider what happens if other people make the same request. Sometimes, public hearings are involved.

Speak to a local attorney who's familiar with zoning regulations in your area. If you just put up your sign and encourage the vehicular traffic without following the proper channels, you could get yourself--and your landlord--in a lot of legal hot water.