How did dynasties replace each other?

Answer 1

In the last years of dynasties, there were always a few warlords who were formerly subordinate to the central government but remained unsatisfied with the current arrangements. They took the chance of managerial disfunction caused by political corruption and social unrest in relation to local revolts, declared independence and hostility to their old master, normally in the name of justice which made their ambition and real intention unperceived. After a series of fierce confrontation, old state apparatus was broken, one warlord stood out from his peers and won the competition for the absolute power. Then, it's the time to rectify the address appropriate to the new leader of the country.

Answer 2

They replace each other by starting wars, or if an emperor dies without having a son then someone must be chosen to take over. But mainly by war.