John Calvin gives some great advice:

The greatest need which a man ever has of the spiritual doctrine of our Lord is when His hand visits him with afflictions, whether of disease or other evils, and especially at the hour of death, for then he feels more strongly than ever in his life before pressed in conscience, both by the judgment of God, to which he sees himself born to be called, and the assaults of the devil, who then uses all his efforts to beat down the poor person, and overwhelm him in confusion.

And therefore the duty of a minister is to visit the sick, and console them by the word of the Lord, showing them that all which they suffer and endure comes from the hand of God, and from his good providence, who sends nothing to believers except for their good and salvation. He will quote passages of Scripture suitable to this view.

Moreover, if he sees the sickness to be dangerous, he will give them consolation, which reaches farther, according as he sees them touched by their affliction; that is to say, if he sees them overwhelmed, with the fear of death, he will show them that it is no cause of dismay to believers, who having Jesus Christ for their guide and protector, will, by their affliction, be conducted to the life on which he has entered. By similar considerations he will remove the fear and terror which they may have of the judgment of God.

If he does not see them sufficiently oppressed and agonized by a conviction of their sins, he will declare to them the justice of God, before which they cannot stand, save through his mercy embracing Jesus Christ for their salvation.

On the contrary, seeing them afflicted in their consciences, and troubled for their offenses, he will exhibit Jesus Christ to the life, and show how in him all poor sinners who, distrusting themselves, repose in his goodness, find solace and refuge.

Moreover, a good and faithful minister will duly consider all means which it may be proper to take to console the distressed, according as he sees them affected: being guided in the whole by the word of the Lord.  Furthermore, if the minister has anything whereby he can console and give bodily relief to the afflicted poor, let him not spare, but show to all a true example of charity. (Catechism of the Church of Geneva)

In summary, then, Calvin encourages all Christians, and especially ministers, to keep several things in mind as they visit the sick.

  1. People need the gospel more than ever when they are ill.
  2. Remind the sick from the word of God that God is sovereign over their illness and has sent it for their good.
  3. If the illness is severe, comfort the sick with the sure knowledge that those who die in the Lord have nothing to fear.
  4. If the sick consider their sins to be light and trivial, teach them of the justice of God and call them to embrace the mercy of Christ.
  5. If the sick are afflicted in their consciences, help them find rest in Christ.
  6. Don’t be afraid to bring some small token of physical relief—books, flowers, balloons, games, movies, a homemade card.