There are many Biblical sources that support this Sacrament.

According to Matthew 4: 23-25;

Jesus went throughout Galilee, teaching in their synagogues, proclaiming the good news of the kingdom, and healing every disease and sickness among the people. News about him spread all over Syria, and people brought to him all who were ill with various diseases, those suffering severe pain, the demon-possessed, those having seizures, and the paralyzed; and he healed them. Large crowds from Galilee, the Decapolis, Jerusalem, Judea and the region across Jordan followed him.

In St James' letter to his friends, regarding the anointing of the sick: 

Is anyone among you suffering? He should pray. Is anyone in good spirits? He should sing praise. Is anyone among you sick? He should summon the presbyters (Priest) of the church, and they should pray over him and anoint [him] with oil in the name of the Lord, and the prayer of faith will save the sick person, and the Lord will raise him up. If he has committed any sins, he will be forgiven. (James 5: 13-15)

When to receive the Sacrament of anointing of the sick

1. Before any operation (either major or minor operation) 

2. When diagnosed with any disease. 

3. When you are in the hospital.

4. If you think or sense that are emotionally and spiritually broken or wounded.