It was once told to me that fasting was how the Spirit lets the flesh know who is boss.
:D
Isaiah 58 is a powerful passage on the benefits of fasting. It shows the fast that pleases the Lord, as well as those that are displeasing to him.
1 Kings 13 Tells the story of the old prophet that was called to a fast, then broke it, shows how we should take it seriously when we fast. :o
There is nothing wrong with fasting without being called to it. It is a great way to draw close to the Lord. The Lord does at times call for a fast. He also at times calls for feast and celebrations. Just be sensitive to His voice in the matter.
If you have never fasted before, start very small. JM suggested a 24 hour fast. I would make that the second step, and begin even smaller. Skip one meal.
Take the time that you would have spent cooking, eating, and cleaning up and spend it with the Lord. Use the time with Him and focus on fasting. Tell Him that you want to fast, do a word study. Do some research on it, Take notes. Then ask Him to keep what you commit, and keep you from temptation.
I seem to have developed a system. If I want to go on a long fast, I do several short ones in a sort of series before. It helps rebuild my faith and confidence, then when I go on a long fast, I can focus on more spiritual things.
There are many sources of sabotage that will come at you. If people know that you are trying to fast, you will find offers for food, invitations to dinner, to parties, etc. Many think that getting serious with God is a source of humor for them. Ask God to give you the grace to deal with them. It could also be His way of asking you to pray for them.
When you graduate to longer fasts, you will notice that things that used to go without notice are suddenly magnified. Billboards for restaurants, magazine pictures of cake, etc. Ask the Lord to protect you from anything that would cause you to turn away from your commitment.
In my own life, fasting at first seemed to focus on me, and my relationship with Him. Every fast brought revelation knowledge, healing, and I found that things that were not kosher were purged from my diet. As my faith was built up, I realized that the Lord would call me to fast, rather than my offering it. The fasts would last longer. As I would fast, He would give me burdens for other people. As I prayed for others, He would show me things in their lives that needed His attention. He would allow me to see the answers to prayer, and how He would fix problems that I never knew that they had. Fasting seems to take me to a deeper spiritual realm that can not be reached any other way. God is, even today, doing a work that He showed me during fasts that took place long ago. Some of them twenty years ago, some over forty years ago.
On the practical side, you will get hungry. When you go into a long fast, I believe that you will find that there is a certain level of hunger that you reach, and then you do not get 'hungrier'. Work at focusing your thoughts on the purpose of your fast, and not on your hunger. (Get down to business)
Before beginning a fast, you also need to know the proper way to breaking a fast. You might think that you could sit down to a steak and potato after three days or a week. Don't even think about it. Eat a few crackers and some juice. Your digestive system has been shut down. Forcing food back into it can be painful, and if you are not aware of what to expect, it could send you to the nearest ER.
Continue reading your books, and learn as much as you can. Pray over it. Pray over your prayers. Ask God to give purpose to you. You will draw closer to God.