I've found some pretty interesting cases of exorcisms, including this one I found from The Juvenile Instructor, which quotes David O. McKay's personal journal from when he was 25:
3 September 1898, Newarthill, Lanarkshire, Scotland: Went to Newarthill to see the young girl [Charlotte] who is sick. Found her in a nervous or spasmodic fit. Brother Orr said she was possessed of evil spirits, and indeed it did appear that such was the case. She would laugh and talk [and] tell the priesthood to go home and not torment her, ask their name, etc. Sometimes she would try to rise out of bed and although she was but a lassie weighing less than 100 pounds, it was all I could do to hold her and put her again in a quiet position. She seemed to be entirely unconscious when in this state. Her eyes were closed, and when she spoke, the sound came from her throat–not a lip moved. Just before regaining consciousness, her body became rigid, her hands clenched so tightly that the nails penetrated the skin, and her whole body–every muscle it seemed–became stiff as a board. She would lie in this state and then awaken, weak and limp, entirely exhausted. These attacks came on every few minutes, each one lasting about five minutes or more. We administered to her and she obtained peace for about an hour and half, during which time she sat up and talked as intelligently as anyone. She had another spell before we left. (We were then fasting for her relief).Interesting, n'est pas?
4 September 1898: After meeting [in Airdrie] we walked five miles back to Newarthill where, after a forty-eight hour fast, we were going to rebuke the evil power–whatever it was–afflicting the girl. The fast meeting was held in Sister Major’s house. As we entered, Charlotte was suffering from another attack. She had walked from Brother Orr’s–about a quarter or half mile. As the meeting commenced, the attacks became more frequent. One elder had to hold her all the time. These spells continued until after she partook of the sacrament. She then had peace during the meeting until we were about to unite in prayer before administering to her. Just as we began to consecrate the oil, she went into one of these fits–or had another attack. This was a long one. I told the saints (the house was full) that we would all kneel around her and unite with the one who was mouth in prayer. Taking her in my arms, I took a seat in the center of the room. When she regained consciousness, I told her we were all going to pray for her and asked her to unite with us. She feebly answered that she would. Brother Leatham was mouth. At the conclusion she said ‘I can walk now.’
Upon researching this topic, I've come up with some questions: Usually in movies, and in the most famous cases of exorcism, it's a Catholic Priest performing the exorcism, while the person inhabited by some evil force is restrained in some way. The Priest usually uses holy water and the same prayer over and over again. What is the LDS process of exorcism? In the Old and New Testament, when there is a claim that someone is inhabited by an evil spirit, does it mean that that person is just mentally unstable, or does it mean that person is literally possessed? As LDS Doctrine dictates, the only way something can be done in the name of Christ is through the Priesthood, something which members of the LDS Church believe only our Church holds. If this is the case, how have other people of other religions performed exorcisms? Or have they really? If exorcisms in the LDS Church do happen, how often? And why aren't they discussed very much?