Fasting means to not ingest or take in any food or any water for a particular period of time. We find this definition in the book of Esther, where the Queen asks her uncle Mordecai to request others not eat for her.
. . . fast for me, and do not eat nor drink three days, night or day. My maidservants and I will also fast in the same way (Esther 4:16).
Fasting and who should and should not do it was something that puzzled the disciples of John the Baptist. They made a special trip to ask Jesus about his views regarding the subject. The Lord did not hesitate to tell them that there is a time to perform this act and a time to refrain from it.
And Jesus said to them, 'Are the children of the bridechamber able to mourn while the bridegroom is with them? But the days will come when the bridegroom shall be taken away from them, and then they shall fast.' (Matthew 9:15, HBFV).
Biblical fasting is carried out for at least a day or more. As is hinted at in the Esther quote above, a complete day is considered from sunset of one day to sunset the next day.
Why Do It?
One reason why occasional fasting is part of being a Christian is that we live in an evil world. If we are not careful, we can be lured into indulging in sin just like those who are not converted. We must be like Lot, who Peter said withstood the evil influences around him that came from living in Sodom and near Gomorrah (2Peter 2:7 - 8).
We need to maintain a close, personal relationship with our Father in heaven if we are to have any chance at resisting evil. Fasting, meaning abstaining from food and water, draws us into a closer relationship with God and sharpens our focus to seek His perfect will in our daily lives.
Sometimes fasting is needed in order to petition God and to seek his favor for others. The early New Testament church abstained from food and water in order to effectively pray for Paul and Barnabas' ministry (Acts 13). They also did so when choosing leaders in the church (Acts 14:23). David refused any food or drink in the hope of saving the life of his baby through Bathsheba (2Samuel 12:15 - 16, 22).
Lastly, contemporary dietary science is only now becoming aware of the health benefits of fasting. Recent studies done at the United States National Institutes of Science indicating that longer life, resistance to diabetes and other illness and better weight control are the results of a moderate program of going without food from time to time.
How Often?
Christians are commanded by God to fast at least one day a year, during the holy day known as the Day of Atonement (also called Yom Kippur - Leviticus 23:32). We should, however, try to fast a few additional times each year like the Apostle Paul (2Corinthians 11:27). Jesus did not eat or drink for forty days so that he could fully resist the temptations of the devil. We should go without food and water whenever we feel the need to seek God.
Preparation
The first thing one should do is stop drinking anything with caffeine in it, coffee, regular black tea (herbal teas may be beneficial) or soda pop in the week preceding a fast. Instead, one should drink pure filtered water just before you begin so you will be adequately hydrated and will not get a headache or other ailments.
With certain kinds of health conditions (such as diabetics, etc.), you should consult with a doctor or other medical professional before going, for any period of time, without food or water.
Fasting is meant to be a private act between us and God. We are warned by Jesus himself not to be proud of or boast to others that we fast in the hope they will think we are 'spiritual' and close to God (Matthew 6:16 - 18).
It is also important to remember that a fasting is not an end unto itself. It should draw us close to God and focus our minds to think like he does. But it should ultimately lead us to help those who are oppressed, feeding those who are hungry, providing shelter for those who have none, and giving clothes to those who are in grave need (Isaiah 58:6 - 7).