A change in zoning is called "rezoning". Whether requested by a property owner or by the local government, rezoning changes often involve changing a parcel or parcels of land from one land use classification to another land use (i.e., from retail use to restaurant use, agricultural use to light industrial, low density to high density).
Not all rezoning proceedings are alike. But key features are consistent. For starters, it begins with an application (and payment of a fee), followed by notice to all nearby property owners. Several open public hearings—some at the neighborhood level--are held so that area residents and government agencies can speak out their opinions and concerns.
Most people seeking a rezoning retain an experienced attorney to assist them. At the public hearing, she or he would "present your case" and be prepared to handle the objections that might be expected from those who oppose your request. A lawyer will also be prepared to allay the fear of opponents that the requested zoning change could hurt property values or be incompatible with the surrounding uses of nearby areas and the goals of the city’s comprehensive community plan.