What methods of rule did European use to govern foreign peoples?

They directly governed, or indirectly governed them. They also used the sphere of influence to, well, Influence them xD.

Have a wonderful rest of the day.

One method of rule Europeans used to govern foreigners was religion. They used religion to instill fear in those who had not been exposed to Catholicism or Christianity by telling them they would go to hell if they did not act, talk or live a certain way.