When Jesus was speaking about fasting and prayer - He was referring to a Spiritual fast where we abstain from selfishness and selfish desires.

Isaiah 58:3-6 KJV — 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. 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. 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? 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?

Yet, if you still desire to fast carnally - the best way to do it is with a juice fast.

Mark 9:28-29 KJV — And when he was come into the house, his disciples asked him privately, Why could not we cast him out? And he said unto them, This kind can come forth by nothing, but by prayer and fasting.

Psalm 35:13 KJV — But as for me, when they were sick, my clothing was sackcloth: I humbled my soul with fasting; and my prayer returned into mine own bosom.

Romans 8:5-8 KJV — For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit. For to be carnally minded is death; but to be spiritually minded is life and peace. Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be. So then they that are in the flesh cannot please God.