Each time a Christian falls seriously ill, he/she may receive the sacrament of the Anointing of the Sick, and may receive it again if the illness should worsen. The celebration of the sacrament of the Anointing of the Sick consists essentially in the anointing of the forehead and hands of the sick person. The anointing is accompanied by the liturgical prayer of the celebrant asking for the special grace of this sacrament.
Only priests (and bishops) can give the sacrament of the Anointing of the Sick, using oil blessed by the bishop, or if necessary by the celebrating priest himself. The priest of the Church—in silence—lays hands on the sick; he prays over them in the faith of the Church. He then anoints them with blessed oil.
Anointing is a liturgical and communal celebration, regardless of whether it occurs within a church or not. It is certainly fitting to celebrate it within mass. It can be preceded by Penance and followed by the sacrament of the Eucharist.