There is no one way rulers come into power. In light of this, examples would be best.
First, some rulers come into power by conquest. When Caesar defeated Pompey, the issue was settled. The most powerful man in Rome would be Caesar. Military might sometimes settles things in a definitive way. In the same way, Octavian came into power when he defeated Antony at the battle of Actium. The same can be said for Cyrus and many others.
Second, some rulers come into power, because leadership is passed down within the family. For example, any hereditary monarchy works this way. David passed down leadership to Solomon in the Bible. The Tudors in England did the same thing.
Third, other ruler comes into power by elections. This is how American and many other democracies work today. Presidents and prime minister are elected.
Thinking about rulers in these diverse ways should show you that there is no one way rulers come into power.