I am wondering what the Church’s stance is regarding exorcisms. Do they believe in possessions? If so, what is done about it?
Because there are examples in Christ’s time of possessions, the official stance of the Church is that they are real, and they do occur. Just as Christ expelled demons from people, there are examples of Joseph Smith doing the same in the name of Jesus Christ.
As a rule, most of the operations of the Priesthood are not broadcast to the world. The Priesthood is intended as a tool to allow the power of Christ to operate more fully among God’s children. Most of the things the priesthood is used for are personal in nature, whether personal blessings, father’s blessings, or advancement in the Priesthood to a higher office. Very few people actually participate in any given ordinance with the notable exception of the Sacrament.
While I’ve never participated in one, I believe exorcisms are performed today using the same priesthood authority the Disciples used during Christ’s ministry on earth. It was given to them for that purpose then, and we have the same authority today.