A rezoning, also called a zoning map amendment, moves a property from one zoning district to another. It is usually needed when the use or the density you want is not allowed in the current district, and no variance or special exception can grant it.
Most places follow the same path. Start with a meeting with the planning staff, who will say whether the change fits the comprehensive plan and what the application needs. File the application with the fee, a survey or legal description, and often a concept plan. Staff review it and write a recommendation, and the hearing is advertised to the public and to nearby owners.
The planning commission holds a public hearing and votes to recommend approval or denial. The governing body, the city or town council or the county commission, then decides, often after a second hearing and, in many places, more than one reading of the ordinance. Some places offer a conditional or planned development rezoning, which ties the new district to a specific plan or conditions.
What decides it is usually consistency with the comprehensive plan, the staff recommendation, the commission's vote and the neighbors' response at the hearings. Talking with neighbors before filing, and fitting the request to the plan, matter more than the paperwork. In Charleston, South Carolina, for example, as elsewhere in the state, the planning commission recommends and the council decides.