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/premier/etc. is the player who owns the most parcels in their state/province/etc. To become governor/premier/etc., purchase parcels in your state/province/etc. The player who owns the most parcels in that state/province/etc. will become governor/premier/etc. The president/prime minister/etc. owns the most parcels in the their country. To become president/prime minister/etc., purchase parcels in your country. The player who owns the most parcels in that country will become president/prime minister/etc. Players can hold a title in more than one region (i.e. be mayor of multiple cities).
If you are playing from somewhere other than the United States, click here to find out what the VIP titles are in your country and what their jurisdictions are called.