What is Fasting?
Fast: Strong's # 3522
: to abstain as a religious exercise from food and drink; either entirely, if the fast lasted but a single day, or from customary and choice nourishment, if it continued several days.
Dictionary: To abstain from all food - To eat only sparingly or of certain kinds of food, esp. as a religious observance - A fasting; an abstinence from food, or a limiting of one's food, esp. when voluntary and as a religious observance.

We fast to bring our bodies into subjection and to be more sensitive to the Spirit of the Lord.
After Jesus had fasted 40 days and 40 nights the Bible says in Luke 4:14, And Jesus returned in the power of the Spirit into Galilee.
Now I am not saying we have to fast 40 days and 40 nights.
The length of the fast is up to the individual. Some people fast one meal a day. Others fast certain foods that they really like to eat. Some fasts may be a whole day or many days.
But....when we fast we should spend as much time as possible with the Lord: Bible study, meditating on God's Word, and prayer.
Example: If you have to work, use your lunch break, instead of eating, in fellowship with the Lord.

In the Old Testament (Exodus 24:38) Moses fasted 40 days & 40 nights when he was in the mountain with God. His face shone when he came back down (Exodus 24:39), because he had been in God's presence.

Examples of Fasting:
Old Testament: Judges 20:26 - I Samuel 7:6 - I Samuel 31:13 (7 days) - 2 Samuel 1:12 ( 'till evening) - 2 Samuel 3:35 - 2 Samuel 12:16-18 (7 days) - 2 Chronicles 20:3 - Ezra 8:21 - Nehemiah 1:4 - Nehemiah 9:1 - Esther 4:3&16 - Psalm 35:13 - Psalm 69:10 - Psalm 109:24 - Jeremiah 36:9 - Daniel 6:18 - Daniel 9:3 - Joel 1:14 - Joel 2:12-15
New Testament: Matthew 4:2 - Matthew 9:14-15 - Matthew 15:32 (3 days) - Mark 2:18-20 - Mark 8:2-3 ( 3 days) - Luke 2:36-37 - Luke 5:33-35 - Acts 13:1-3 - Acts 10:30 - Acts 14:23 - Acts 27:33 (14 days) - 2 Corinthians 6:5 -
2 Corinthians 11:27

Some of the fasting in the Old Testament was done to see if God would change His mind about punishment, etc.
2 Examples: Nineveh (Jonah 3:5-9) - David ( II Samuel 12:14-23 )
In I Kings chapter 21 is an example of the wrong kind of fast.
First Ahab fasted because he was pouting ( I Kings 21:4-5), then Jezebel called a fast so she could set up Naboth with false witnesses and have him killed (I Kings 21:9-10 ) .

1 Kings 21:27 (Elijah prophesied the fate of Ahab & Jezebel, vs. 17-24)
After hearing Elijah, Ahab truly fasted & repented.
27And it came to pass, when Ahab heard those words, that he rent his clothes, and put sackcloth upon his flesh, and fasted, and lay in sackcloth, and went softly.
28 And the word of the LORD came to Elijah the Tishbite, saying,
29 Seest thou how Ahab humbleth himself before me? because he humbleth himself before me, I will not bring the evil in his days: but in his son's days will I bring the evil upon his house.

Isaiah chapter 58 is about fasting; The wrong kind, the right kind, and the blessings of the right kind of fast.
Isaiah 58:3 Wherefore have we fasted, say they, and thou seest not? wherefore have we afflicted our soul, and thou takest no knowledge? Behold, in the day of your fast ye find pleasure, and exact all your labours.
4 Behold, ye fast for strife and debate, and to smite with the fist of wickedness: ye shall not fast as ye do this day, to make your voice to be heard on high. (Hypocritical fasting)
5 Is it such a fast that I have chosen? a day for a man to afflict his soul? is it to bow down his head as a bulrush, and to spread sackcloth and ashes under him? wilt thou call this a fast, and an acceptable day to the LORD?
This is the fast that God has chosen.
Isa 58:6 Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke?
Isa 58:7 Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?
This is the blessing of that fast.
Isa 58:8 Then shall thy light break forth as the morning, and thine health shall spring forth speedily: and thy righteousness shall go before thee; the glory of the LORD
shall be thy rereward.
Isa 58:9 Then shalt thou call, and the LORD shall answer; thou shalt cry,
and he shall say, Here I am. If thou take away from the midst of thee the yoke, the putting forth of the finger, and speaking vanity;
Isa 58:10 And if thou draw out thy soul to the hungry, and satisfy the afflicted soul; then shall thy light rise in obscurity, and thy darkness be as the noon day
Isa 58:11 And the LORD shall guide thee continually, and satisfy thy soul in drought, and make fat thy bones: and thou shalt be like a watered garden, and like a spring of water, whose waters fail not.
Isa 58:12 And they that shall be of thee shall build the old waste places: thou shalt raise up the foundations of many generations; and thou shalt be called, The repairer of the breach, The restorer of paths to dwell in.
Isa 58:13 If thou turn away thy foot from the sabbath, from doing thy pleasure on my holy day; and call the sabbath a delight, the holy of the LORD, honourable; and shalt honour him, not doing thine own ways, nor finding thine own pleasure, nor speaking thine own words:
Isa 58:14 Then shalt thou delight thyself in the LORD; and I will cause thee to ride upon the high places of the earth, and feed thee with the heritage of Jacob thy father: for the mouth of the LORD hath spoken it.
Another example of hypocritical fasting.
Zechariah 7:5 Speak unto all the people of the land, and to the priests, saying, When ye fasted and mourned in the fifth and seventh month, even those seventy years, did ye at all fast unto me, even to me?
They weren't fasting unto God, they were just doing something religious.

Matthew 6:16 is another example of the wrong kind of fast.
Matthew 6:16 Moreover when ye fast, be not, as the hypocrites, of a sad countenance: for they disfigure their faces, that they may appear unto men to fast. Verily I say unto you, They have their reward.
This is the way to fast.
Mt 6:17 But thou, when thou fastest, anoint thine head, and wash thy face;
Mt 6:18 That thou appear not unto men to fast, but unto thy Father which is in secret: and thy Father, which seeth in secret, shall reward thee openly.
Notice He said WHEN you fast, NOT IF you fast.
Fasting, along with prayer, is important. Some demons won't come out unless we have fasted
& prayed.
Matthew 17:21 Howbeit this kind goeth not out but by prayer and fasting.
Mark 9:29 And he said unto them, This kind can come forth by nothing, but by prayer and fasting.

Fasting regarding husbands & wives.
1 Corinthians 7:5 Defraud ye not one the other, except it be with consent for a time, that ye may give yourselves to fasting and prayer; and come together again, that Satan tempt you not for your incontinency.
 I think the Amplified Bible makes this scripture a little plainer.
Amplified Bible: 1 Corinthians 7:5 Do not refuse and deprive and defraud each other (of your due marital rights), except perhaps by mutual consent for a time, so that you may devote yourselves unhindered to prayer. But afterwards resume marital relations, lest Satan tempt you (to sin) through your lack of restraint of sexual desire.
Don't brag about how you fast. That is the wrong way to act.
Luke 18:10 Two men went up into the temple to pray; the one a Pharisee, and the other a publican.
Lu 18:11 The Pharisee stood and prayed thus with himself, God, I thank thee, that I am not as other men are, extortioners, unjust, adulterers, or even as this publican.
Lu 18:12 I fast twice in the week, I give tithes of all that I possess.
Lu 18:13 And the publican, standing afar off, would not lift up so much as his eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner.
Lu 18:14 I tell you, this man went down to his house justified rather than the other: for every one that exalteth himself shall be abased; and he that humbleth himself shall be exalted.

This is a subject alot of people don't like to talk or think about.  Jesus told us to do it.  He said WHEN you fast.  If we fast unto the Lord, and not just because it is a religious ceremony, fasting can be a very rewarding experience.