As a Christ-follower, I have heard several different ways fasts are to be done as well as several different purposes.
The other day, however, I was listening to the Daily Audio Bible (I still recommend this by the way) and heard Isaiah 58 and God's perspective on Israel's practices of fasting. From "The Message":
1-3 "Shout! A full-throated shout! Hold nothing back—a trumpet-blast shout!
Tell my people what's wrong with their lives,
face my family Jacob with their sins!
They're busy, busy, busy at worship,
and love studying all about me.
To all appearances they're a nation of right-living people—
They ask me, 'What's the right thing to do?'
and love having me on their side.
But they also complain,
'Why do we fast and you don't look our way?
Why do we humble ourselves and you don't even notice?'
3-5"Well, here's why:
"The bottom line on your 'fast days' is profit.
You drive your employees much too hard.
You fast, but at the same time you bicker and fight.
You fast, but you swing a mean fist.
The kind of fasting you do
won't get your prayers off the ground.
Do you think this is the kind of fast day I'm after:
a day to show off humility?
To put on a pious long face
and parade around solemnly in black?
Do you call that fasting,
a fast day that I, God, would like?
6-9"This is the kind of fast day I'm after:
to break the chains of injustice,
get rid of exploitation in the workplace,
free the oppressed,
What I'm interested in seeing you do is:
sharing your food with the hungry,
inviting the homeless poor into your homes,
putting clothes on the shivering ill-clad,
being available to your own families.
Do this and the lights will turn on,
and your lives will turn around at once.
Your righteousness will pave your way.
The God of glory will secure your passage.
Then when you pray, God will answer.
You'll call out for help and I'll say, 'Here I am.'
I don't know if this is the only answer to what a fast is to be like. I don't think so. I do believe that the purpose of fasting is to "get something" from God for yourself, although, that may be a result.