Fasting is learning freedom from food and how God directly nourishes us.
Prayer is conversation with God.

While they were worshipping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.” So after they had fasted and prayed, they placed their hands on them and sent them off.
Acts 13:2-3

Devote yourselves to prayer, being watchful and thankful.
Colossians 4:2

Fasting forces us to take attention from our desires in order to focus on God. Jesus tells his disciples that his food is to “do the will of him who sent me and to complete his work” (John 4:34). Fasting can be a humbling experience, as we see just how controlled we are by our appetites. But it also teaches us that what sustains us is not the food we eat or the pleasures we feel, but God alone. 

Richard J. Foster

The Christian Vocation is to be in prayer, in the Spirit, at the place where the world is in pain, and as we embrace that vocation, we discover it to be the way of following Christ, shaped according to his messianic vocation to the cross, with arms outstretched, holding on simultaneously to the pain of the world and the love of God.

N.T. Wright

Suggested Reading:

Fasting: The Ancient Practices (book)  by Scot McKnight

Understanding Prayer (article) by Richard Foster