its quite an easy process actually.

First you must gain 15000 in game /balance and apply for resident.

at that point, you can either join a mayor by being their co-mayor, or wait until you have $85000 in your /balance at which point you can apply to be mayor. With applying for mayor, you roam the lands of the main world in search for an ever elusive 100x100 to 200x200 area to call your own. You place 4 signs, one on each extreme corner of land, then include those coordinates in your mayor app.

After you apply, make sure to keep 85000 in your balance til approved. within 24-48 hours, you should turn from a nice light green to a mayoral dark green and have a protected area to call your own!

 

In addition to what Alarah said, you can look here for information on how to submit the application once you have earn the 85k. Here is the link for making a resident application.