Dear Preacher -
Jesus dealt with demon possession via exorcism. The demons in the person whose being was captured by demonic evil forces were expunged. Jesus' mode of operation was to rebuke and or expel the demons.
He would command it, and it was done (Matt. 9:33, Mk. 1:25, Lk. 7:29).
Jesus confronted demons and demon possession as he exercised ministry and proclaimed that the Kingdom of Heaven was at hand.
It was never a specialist ministry, done as an event on its own. It was not done to draw attention to himself. In fact, he would, after exorcism, retreat to a solitary place (Mk. 1:32-39).
And he refused to give the Pharisees a sign (Mk. 8:11-13).
Jesus did not use any magical formula or aids to accomplish the act of deliverance. His way was to address the demons with an authoritative, confrontational command. Jesus attributed the effectiveness of his action to the Spirit of God (Mt. 12:27).
The demons were afraid of Jesus and seemed unable to tolerate His presence. As the saying goes, 'demons will have to flee'. Jesus never appeared threatened by demons.