Dedicated to the Lord Jesus Christ Who loved us, gave Himself for us, and washed us from our sins in His own Blood; and to the Church, which is His body.

MATTHEW 6:14-18 
Jesus is saying that there should be no external sign of fasting or sorrow, but it should be done secretly to the Lord to receive full reward. Paul stated in 1 Corinthians 7:5, that abstinence from the physical relationship in marriage for the purpose of fasting should not be done without the consent of one's spouse.
A fast does not always have to be totally secretive to be productive. Jesus is dealing with the motives behind our actions. The fast must be directed toward God and not men.
Fasting accomplishes many things. One of the greatest benefits of fasting is that through denying the lust of the flesh, the spirit man gains ascendancy. Fasting was always used as a means of seeking God to the exclusion of all else.
Fasting does not cast out demons, but rather, it casts out unbelief. Fasting benefits every aspect of the Christian life - not only in the casting out of devils.
The real virtue of a fast is in humbling ourselves through self denial, and it can be accomplished through ways other than total abstinence. Partial fasts can be beneficial, as well as fasts of our time or pleasures.
But, because appetite for food is one of man's strongest drives, fasting from food seems to get the job done the quickest. Fasting should be a much more important part of our seeking God. Endeavor to live a fasted lifestyle, whether it is a denial of yourself through food, or denial of your own wishes. Exalt Jesus, put Him first in everything.