Matthew 17:21 "Howbeit this kind goeth not out but by prayer and fasting."
There are many examples in the Word of God of men who fasted and prayed. Moses did for forty days. Daniel did for three weeks. Paul did for three days. The church at Antioch also fasted and prayed for the will of God. These are normal people who had a strong desire to see God's will done.
Fasting is a sacrifice that a person makes for prayer and seeking God and not for what the individual wants. It is our way of showing God that we're willing to sacrifice food for our bodies (or whatever God leads to sacrifice) in order to let God know what we're praying for is most important.
Fasting is not something that is preached about or encouraged much less being done in people's lives today. Usually when fasting is mentioned to someone they tend to think the person telling them about it is nuts. However...there are some prayer requests that will only be answered by prayer and fasting.
Fasting is a spiritual commitment that is more important to us than food.
Looking at the examples I gave at the beginning of the post we can see there are different length of time for fasting. It is also something that we don't just decide to do. Fasting is something that is led of God. God will tell a person how long and how to fast. There are complete fastings where the person fasts completely except for water. Our bodies need water so I don't believe God would ask that kind of fast where we give up water. But He can ask a person to fast all meals for a period of time.
Then there are different kinds of partial fasts. There are fasts that you might give up one or two meals a day. God may lead you to give up your favorite drink or food that you eat every day. He may ask you to fast your one thing you love to do each day whether it be computer time or your exercise time or something like that. During those times you would be doing those things you would get alone with God to pray and seek God.
Fasting is not just something a person decides to do. God places it on the heart of a person to do it. If it is a God-led fast then He will sustain and strengthen you no matter how long the fast is. If it is a self-led fast you will not stick with it. So if you are one that says you cannot fast...you can...if God is leading you to. And if He is leading you to...you better do it or you may never see that prayer answered that God desires to answer as a result of that sacrifice you would be making.
So there is no misunderstanding...you must know that ANYTHING we try to do for God that the enemy will be right there trying to make things hard to do it and make you come away from doing as God has told you to.