Since the modern Bible versions based on the corrupt Alexandrian manuscripts (such as the NIV, ESV, NASB, etc.) excise the word fasting from the Word of God it will follow that there is little knowledge or understanding of the central practice of fasting among the mainstream that so devotedly champions the defiled Bibles.
Check the King James Version against your favorite modern version to see how the word - and hence the central Biblical practice of - fasting has been deleted from Matthew 17:21, Mark 9:29, Acts 10:30, and 1Corinthians 7:5.
Prayer and fasting and engaging the Word of God are the primary practices of a Christian. On a foundation of regeneration and faith and repentance. All other Christian practices are contained in the engaging of the Word of God, prayer, and fasting (prayer and fasting correspond, for instance, in practical ways to the two great commandments of Jesus to love God and love your neighbor as yourself). Notice these are the three practices that mainstream Christians have the most difficulty with? Some have even come to mock the notion of reading the Bible. Prayer is not even understood by Christians, really to any degree; and they get little to zero help from their teachers on this subject. They just sort of maintain a quiet, confused or sceptical state on the subject and practice of prayer (and even when they do do it in it's meaningful and plain sense they don't know why it is something that is real and meaningful). Fasting isn't even on the radar of mainstream Christians. I'll write about prayer later.
Fasting...
That means...going without food for a certain amount of time?
Yes.
And that's it?
No.
Physically, fasting is a practice that involves control. Control of physical desires, period. Food, sex, laziness (and throw in out-of-control talking). You either have control over these things or they have control over you. Observing an amount of time where you take in no food; or provoking no orgasm; or practicing silence of the tongue is all the act of fasting, regarding your physical nature.
It's about inner command. Do you have control of something or does it have control of you? Fasting from physical indulgences also achieves other things. It takes you out of your mechanical habits and patterns of activity and forces you to confront yourself and reality - emotionally and intellectually - in ways that the average person would just rather avoid.
Other kinds of fasting...
Fasting from indulging in common, negative emotional behaviour such as the indulging of resentment or indignation or anger or even annoyance. (This is a difficult type of fasting.) Most Christians have never even been made acquainted with the very idea that not all emotions are of equal value. Resentment is 'just what humans feel'. In fact, the world wants you to indulge resentment. It encourages you to be resentful. It's noble to be resentful! All the actors in the movies and television programs are being resentful about something most of the time. It's human! It's weird not to be resentful...
Resentment is a word and feeling that, more than any other, collects most all of what glorifies the world, the flesh, and the devil in terms of emotional behaviour. To fast from indulging resentment is a very real, and Christian, kind of fasting. Christian because as a Christian your aim is to glorify God, not the world, the flesh, and the devil. Gratitude is the opposite of resentment, and it is gratitude that glorifies God. It is gratitude that is involved in being able to turn the other cheek, or to give your shirt as well when your coat is demanded of you. Gratitude that you are an heir of the Living God, in the Kingdom of God, a stranger in this world, and you are experiencing both what you deserve (everything that happens to us we deserve) and what your King told you you would experience if you followed Him. (Always needed disclaimor: self and national defense is very Christian too because God didn't tell you to turn your neighbor's cheek; and Christianity is not a suicide pact...)
The deeper aspect of this kind of fasting is defined in the word separation. Sanctification is separation. Inner separation from indulging self-will to acting from God's will, and external separation from the world.
I could use more practical and closely defined language to describe this, but not in this venue. I just state that to let anyone reading this know that this teaching exists and it's not contained in systematic theology but it is contained in practical theology (and Practical Theology is not, as the academics and book publishers will tell you, about how a pastor should deal with a church member who is exibiting a drinking problem, and other problems of pastoral care)...
The other kind of fasting deals with the intellect. The devil's kingdom is powerful because it is a vast palace of illusion. It's a dank, dark prison, and if it didn't cast a fascinating flood of illusions into its subjects people might catch on to it. The devil's kingdom also numbs its prisoners with various drugs (see 'physical fasting' above).
By the way: one of the strengths the devil has over his prisoners is once you start to awaken you are confronted with the reality of being in the devil's prison and that is a depressing, usually always an almost overwhelmingly depressing, realization; so the natural reaction is to go back asleep to it all. Many people experience this reaction when just being presented with anything Christian (the Bible, theology, etc.). It gives them black thoughts and depression and they want to get away from it. Even most committed Christians only go so far and have to medicate with their favorite worldly pastimes, so they never really awaken to the prison they are in.
Fasting is for warriors who can and willingly do face the dark reality of their situation; and overcome. This is part of assaulting heaven. (And assaulting self and the devil...which is why the devil wants mention of fasting out of the Word of God...)
But back to the intellectual kind of fasting... It's the most difficult to describe. Let me just give one example from the activity of reading: when you read a genre novel, let's say a thriller, it is pulling you in. You don't have to make much effort at all to read it. You are fascinated with it. It moves fast and keeps your interest in a shallow way. Now pick up Thucydides' History of the Peloponnesian War. Suddenly the pages aren't turning so fast. Now you have to provide the incentive to read each word and sentence and agonizing page. You have to concentrate and hold your attention to a degree that the thriller just doesn't demand. It's like intellectually going from reclining on a couch to running a mile.
When you were reading the thriller you were 'lost' in it. It 'captured' you. This is what a good movie will do too. You lose yourself in it and in the story and characters. (I mean 'good movie' in terms of the popular notion of what a good movie is.)
To fast from the world intellectually is to not allow yourself to be in a state of being captured by the impressions and influences - and illusion - of the world. It's a pulling back, and being contained, and being conscious of a sort of double attention: attention on what you are experiencing with your senses, and attention directed back at yourself and being awake to the fact of what you're experiencing with your senses. Thoughts as well.
Being the one person in the movie theatre that sees the screen. As opposed to being lost in the moving images and lights on the screen.
The above is not enough for a person to understand these practices fully, yet they are enough to get a good sense that there is more to fasting than the mainstream currently suspects, if indeed the practice of fasting has ever even been on the radar of mainstream Christians...
For biblical documention of these inner, practical level teaching of the Faith you just have to begin to practice it and to see that it is in the very heart of what Jesus Himself teaches throughout the Gospels. When Jesus tells you to be watchful, you will know at a deeper level - a practical level - what He is saying. When He tells you to love your enemy, you see that at more than a shallow, moralizing level. Even when Paul tells you in Romans to awaken out of sleep, you'll be bold enough to recognize he is not talking about head-on-pillow sleep...