Donald Whitney writes on the Discipline of Fasting:

How often do you think fasting is mentioned in the Bible? By my count, there are so me seventy-seven biblical references to fasting. Do es that surprise you? Despite so many references, fasting is not a frequent subject in pulpits, publications, and Christian conversation.

In part, this may be due to the fact that, while fasting may be done cooperatively with fellow believers (as in Acts 13:2), typically it is private in nature and shouldn’t be evident to others (Matt. 6:16–18). So it’s possible that Christians around us fast more than we realize or hear mentioned. But could the main reason that fasting is seldom taught be that fasting is seldom practiced?

Should Christians Fast Today?
As a result of the famine of teaching on the subject, there are a number of common misunderstandings among believers about the discipline of fasting. One is the idea that it is a practice relegated only to biblical times or to religious eccentrics. But Jesus, when asked why His disciples never fasted, replied, “The days will come when the bridegroom is taken away from them, and then they will fast” (Matt. 9:15). Until the ascended Bridegroom returns for His bride, fasting is a spiritual discipline His disciples will occasionally practice. This was the understanding of Christians in the book of Acts, who are reported fasting in 13:2 and 14:23. And church history reports that since the days of the New Testament, the followers of Jesus have likewise engaged in fasting.

Fasting and the Gospel
Another misconception about fasting occurs when people fail to associate it with the gospel. The most egregious version of this is the belief that fasting can impress God enough that He will open the door of heaven for those who deny themselves in this way. That, of course, implies that the life and death of Jesus are unnecessary (“Why repent and trust in Jesus? Just fast a little and heaven is yours.”), which is the greatest possible insult to the Father. Neither fasting nor anything else we could do — no matter how painful, self-sacrificial, or unselfish — can atone for our sins and reconcile us to God. Only Jesus, who offered Himself as a sinless sacrifice to bring others to God, can do that.

But it is also possible for genuine Christians to fast but fail to associate their fast with the gospel. They may fast simply in an effort to get things from God. In the New Testament, however, fasting is related to the spread of the gospel or the fruit of the gospel. Similarly, New Testament believers today should fast in a way connected with the spread of the message of Jesus or fast as those who are the servants of Jesus.

So a Christian might fast, for example, and connect it with prayer for missionary labors, for the Sunday morning sermon, or for his witness to a friend. He might fast with prayer primarily for a personal concern, but rest his confidence that God will answer, not on the basis of his abstention from food, but on the fact that he fasted and prayed in the name of Jesus.

So the error on one side is failing to fast at all, and on the other, fasting with confidence in the work of fasting rather than in the work of Christ.

Fasting for a Biblical Purpose
From the pragmatic perspective, the most common oversight is to fast without a clear biblical purpose. When you become aware of your hunger while fasting, you often remember, “Oh yeah, I’m hungry because I’m fasting.” Your next thought should be something like this: “And I’m fasting for this purpose.” There are at least ten purposes in Scripture for fasting, and most relate to prayer. So your hunger actually serves you during a fast in that it is a constant reminder about your biblical purpose, in this case to pray.

Fasting has to be a discipline, otherwise it is a blessing we’ll never experience. When should you fast? Times of special need, when important decisions must be made, or occasions when spiritual longings are especially intense, are often promptings to enter into a fast. But Christians are free to experience the blessings of fasting as often as they desire. Fasting expresses in a God-ordained way our belief that we have tasted and seen that the Lord is good (Ps. 34:8) — so good that there are times we’re satisfied to feast on Him instead of the food that the Lord made for us to live on. Fasting is a temporary physical demonstration that we believe the truth declared by the gospel, namely that, “Man shall not live by bread alone, but by every word that comes from the mouth of God” (Matt. 4:4). Do you believe that? Do you fast?

From Ligonier Ministries:

http://www.ligonier.org/learn/articles/the-discipline-of-fasting/

See also Spiritual Disciplines for the Christian Life by Don Whitney, (NavPress), p151f.