How were disputes settled in ancient Greece?

Answer 1

By negotiations between the heads of the families involved, who then arranged payment to settle the problem, and if necessary punished their own relatives. And on the unusual occasions if this did not work, physical violence.

On a high level, negotiations between city-states, often with a third city-state acting as intermediary, and if this failed, war.

Answer 2

It depends on the ruler. Some rulers used persicution and their power to minipulate things their way. Others used peace and knowledge to plan for a better tomorow.