How do they get or maintain their power in a monarchy?

Answer 1

In Western countries, they survived mostly by transferring all real power to their Parliament and Governments, a thing that happenend largely in 1848 or shortly after. The royal families that maintained an active involvement in their countries' rule and military affairs almost without exeption did not survive subsequent political upheaval or a lost war; hence the major shake-out after WW 1. Only royal houses that stayed out of active rule and who took on a largely symbolic and ceremonial role as Head of State, survived.

In the (middle) east, surviving royal houses often still do have political power. That is either because they function within a olicharchy or because the King plays a major role in a country's religious traditions.

Answer 2

Monarchies are inherented or taken. The king usually will state he was made king by god.