In the Roman Catholic Church, only a priest or higher rank prelate may perform an exorcism over a possessed person. A priest may only perform an exorcism over a possessed person with the permission of the local ordinary or bishop. This permission may be on a case by case necessity or may be general as was the case in the life of St John Vianney.
Not all exorcisms involve a possessed person and an exorcist is often aided by members of the community during an exorcism. And there is the fact that there are different types of exorcisms which the laity may freely pray.
One can read the rules involved in performing a Major Exorcism here. Rule 19, for example states:
While performing the exorcism over a woman, he ought always have to assisting him several women of good repute, who will hold on to the person when she is harassed by the evil spirit. These assistants ought if possible be close relatives of the subject, and for the sake of decency the exorcist should avoid saying or doing anything that might prove to an occasion of evil thoughts to himself or others.
What types of exorcisms are there in the Latin Rite?
Major Exorcism only applies when there is sound evidence that a person is possessed (Latin obsessis, Italian ossessa, Spanish obsesa).
Only a priest specifically appointed by the Diocesan Bishop (as a general exorcist or to minister to a specific person) may carry out the Rite of Major Exorcism.
The only minor exorcisms specifically published by the Church are those for children and adults preparing for baptism. These may be celebrated by deacons and priests, and also by catechists in dioceses where the bishop has specifically mandated them to do so. Clerics, but not lay catechists, may also use the Oil of Catechumens in the manner set down in the ritual books.
Following the implicit logic of Summorum Pontificum, all priests in good standing have the ability to use the Extraordinary Form rites of blessing and exorcising salt, oil and water. These sacramentals may be given to the faithful for their own private use.
The medal of St Benedict is an important sacramental, the use of which expresses faith in Christ’s protection from the Enemy.
Places and Things
Where there is prudent reason to believe that a place or a thing is under demonic influence, a priest may seek permission from the local Bishop to perform Appendix I of the1999 Rite. Alternatively, (following the implicit logic of Summorum Pontificum), if he has his bishop’s general permission to make use of the Exorcismus in Satanam et Angelos Apostaticos, he may do so without needing to seek explicit permission for the particular case.
It should not be forgotten that simpler remedies – such as blessing the place with holy water (perhaps exorcised using the older Roman Ritual) – or celebrating Mass in the place – may have a powerful effect without needing to have recourse to the Rite of Exorcism. The inhabitants of a place may, of course, make free use of the Appendix II prayers privately. - Exorcism and Prayers for Deliverance: The Position of the Catholic Church
Pope Leo XIII has given permission to use a simple exorcism that may be used by the laity "whenever the action of the devil is suspected, causing malice in men, violent temptations and even storms and various calamities."
Prayer of Exorcism by Pope Leo XIII
A beautiful prayer (a minor exorcism) that anyone can pray to ask Our Lord to drive the lingering influence of Satan away from a
place. Recommended by His Eminence Raymond Leo Cardinal Burke for use by the laity, August 2, 2014. - EXORCISM OF SATAN AND THE FALLEN ANGELS
Years ago the Simple Exorcism for Priests or Laity by Pope Leo XIII was published in a little flyer form which was available in many parish churches. I am still in possession of a few of these copies and have been unable to find more in the last few years. This exorcism is intended to curb the influence of the devil in places or things. The following website shows exactly what was is on the flyers that I have.
Prayer Against Satan and the Rebellious Angels
Published by Order of His Holiness Pope Leo XIII
The following is a simple exorcism prayer that can be said by priests or laity. The term “exorcism” does NOT always denote a solemn exorcism involving a person possessed by the devil. In general, the term denotes prayers to “curb the power of the devil and prevent him from doing harm.” As St. Peter had written in Holy Scripture, “your adversary the devil, as a roaring lion, goeth about seeking whom he may devour.” (1 St. Peter 5,8)
The Holy Father exhorts priests to say this prayer as often as possible, as a simple exorcism to curb the power of the devil and prevent him from doing harm. The faithful also may say it in their own name, for the same purpose, as any approved prayer. Its use is recommended whenever action of the devil is suspected, causing malice in men, violent temptations and even storms and various calamities. It could be used as a solemn exorcism (an official and public ceremony, in Latin), to expel the devil. It would then be said by a priest, in the name of the Church and only with a Bishop's permission.
For the actual text of this simple exorcism see this.