"By the sacred anointing of the sick and the prayer of the priests the whole Church commends those who are ill to the suffering and glorified Lord, that he may raise them up and save them. And indeed she exhorts them to contribute to the good of the People of God by freely uniting themselves to the Passion and death of Christ." (Office of the Catechism, Art V)

The proper time for receiving this holy anointing has certainly arrived when the believer begins to be in danger of death because of illness or old age.  Each time a Christian falls seriously ill, he may received the Anointing of the Sick, and also when, after he has received it, the illness worsens (Catechism, 1528-1529).  Only priests (presbyters and bishops) can give the sacrament of Anointing of the Sick.

In the Anointing of the Sick, the Holy Spirit: unites the sick to the passion of Christ for their good and that of the Church; prepares them for passage to eternal life; grants forgiveness of sins if the person is unable to receive the Sacrament of Penance; restores health if this be God's will (Cf. Catechism, 1532).

It is often said the dying go through the stages of denial, anger, bargaining, depresson, and acceptance.  The Anointing of the Sick helps loved ones release the dying to God and assists the gravely ill to accept death should it be God's will at that time.