The Catechism of the Catholic Church 1526 quotes James 5:14-15: "Is any among you sick? Let him call for the presbyters of the Church, and let them pray over him, anointing him with oil in the name of the Lord; and the prayer of faith will save the sick man, and the Lord will raise him up; and if he has committed sins, he will be forgiven" . This sacrament unites the sufferings of Christians due to serious illness or old age to the saving and healing power of Jesus. People receive forgiveness for their sins and comfort in their suffering and sometimes even physical healing. The priest anoints the forehead and hands of the sick person asking God to grant the person the strength of the Holy Spirit, forgiveness and salvation. It is the right of every Catholic.
The Sacraments of the Church are accompaniments from the cradle to the grave, to strengthen us and unseal for us all the graces which the Lord wishes to bestow on his disciples. Our Lord wouldn't leave us without care and of course he promised to be with the Church always. It is a Sacrament of Jesus' love and mercy when we need it most, so it it important that we don't deprive ourselves or other people of this heavenly opportunities. During his life on earth, he healed the sick, raised the dead, forgave people their sins. It is the same ministry that is continued by the Catholic Church today.
You need to contact your parish priest as soon as the need for it arise - like when you are going on admission to the hospital for a serious illness or even due to old age infirmity or weakness, especially as it gets progressively worse. Otherwise the hospital chaplains can be contacted once in the hospital.
In St Columba's Parish, like in any other parish, we normally visit the sick in their homes, care homes and hospitals and - upon demand - confer the Sacrament. Also we have a mass for the anointing of the sick every second Friday of the month at 1pm in the Sacred Heart Adoration Chapel. See Parish Calendar below.