First, you should consult with the Health Department and / or other agencies, depending on the type and size operation you intend. If you want to operate a simple office from the home as many individuals do these days, no permit is required and to do so is permitted in any residence so long as there is no outside appearance of an office or business operating there and no additional traffic is generated.
Home occupations are only allowed in the Zoning Districts which lists Home Occupation. Planning and Zoning may require more detail on other types of business operations to determine if they are permitted in specific zoning categories so it is best to contact the office at 605-578-3871. Bear in mind that there are distinctly different residential and business zoning categories so there is legislative intent to keep the two uses separate.