Conversion of a population to one religion or the other occurs passively, meaning that the presence of an agent in a province of the opposite religion is enough to slowly bring the population over to his point of view.
A monk or missionary can convert an enemy agent of the opposite religion, causing him to leave his position for a life of religious contemplation. In most case the agent will enter a monastery for a number of turns before returning to his clan capital; in extreme cases he will remain in the monastery indefinitely. Simply select your monk or missionary, right-click on your target agent and select character conversion from the options presented to you.
Incitement to Revolt
Monks and missionaries can incite a population to revolt through their powerful rhetoric. This is always extremely difficult to do in a province where a high percentage of the population follow the same religion as the agent. The subsequent insurrection will always be a peasant revolt, but if the monk incites the peasants they will be joined by Buddhist warrior monks. To incite, simply select your monk or missionary, right-click on your chosen target and select incite from the options presented to you. Remember, there is always a risk that trying to incite revolt will lead to the capture and execution of your agent.
A monk or missionary can demoralise an enemy army, significantly lowering its morale and will to fight through his fiery rhetoric. Simply select your monk or missionary, right-click on your target army and select demoralisation from the options presented to you.
Inspire Castle Town
When inside a castle town belonging to their clan, a monk or missionary will decrease unrest and the chances that the garrison will be bribed. A sense of spiritual calm will be spread throughout the population simply by their presence.