Having been to many Charismatic Masses, the only difference between them and the Ordinary Form of the Mass, is that the people pray in tongues. Some Charismatic Masses may get out of hand, and, yes, I've been to a few of those. But for the most part, they are just an ordinary Mass that incorporates periods where prayer tongues are encouraged. Specifically, after the opening hymn, before the celebrant begins the Mass with the Sign of the Cross, there is a period of prayer with tongues and audible praise and worship acclamations. This repeats itself following the elevation of the host, then the chalice, at the consecration. The elevation is typically extended for several minutes. When the Celebrant lowers the Body and Blood, the prayers cease. I have been present at Masses celebrated by Cardinal Archbishops, where the elevations lasted from 3 to 5 minutes. The sound of the congregation singing and praying in tongues is a beautiful melody.
An authentic Charismatic liturgy should be reverent, respectful, and in conformance with liturgical standards. People should not be dancing, Resting in the Spirit, or engaging in some of the more extreme behavior associated with protestant Pentecostalism. At the archdiocesan-held events I attended, and diocesan-sponsored events, there was typically a praise and worship period before the Mass; you might witness some attendees dancing during this event. Resting in the Spirit typically takes place following the liturgy, as prayer teams and priests and deacons lay hands and pray over individuals. Seminarians attending the events frequently served as catchers for those yielding to Rest in the Spirit. I attended events in very conservative dioceses, Philadelphia and Baltimore. The seminarians were from St Charles Borromeo and Mount Saint Mary's, two of the most orthodox seminaries in the USA. The liturgies were beautiful, the attendees reverent.
The few I had problems with, were common problems that can happen at any OF Mass. Holding hands during the Our Father, standing around the altar in the sanctuary during the Eucharistic Prayer and Consecration, neglect to genuflect before the tabernacle and bow before passing the altar. If you attend in a diocese where the Bishops Office is actively involved with the Renewal, the Mass should be no different than any OF Mass you would normally attend, except for the addition of the audible praying and use of tongues as noted above. A healing Mass is a different liturgy, but it might be a Charismatic Healing Mass. Healing liturgies have an opportunity for the sick to come forward to be anointed by a priest. Charismatic often set up and organize such liturgies.