The mayor is the player who owns the most parcels in their city. To become mayor, purchase parcels within the town border of an incorporated city. You can check city status by opening the location details screen and confirming you are in an official incorporated city.
 
The governor or premier is the player who owns the most parcels in their state or province. To become governor or premier, purchase parcels in your state or province.  The player who owns the most parcels in that state or province will become governor or premier.
 
The president or prime minister owns the most parcels in the their country. To become president, purchase parcels in your country. The player who owns the most parcels in that country will become president or prime minister.
 
Players can hold a title in more than one region (i.e. be mayor of multiple cities).