Our prayers tend to be very random and sporadic. We don't really think about what we are saying and often end up saying either the same thing over and over or saying nothing with real meaning attached to it. When we speak we can't go over it, we can't see what we are saying and so the words slip away from us without thought. The point of this exercise is to help us focus on prayer and prayer that really speaks from our heart and goes straight to God.
This is designed to be done in groups, and especially in a camp setting, but can easily be modified for individuals or other situations.
Give a notebook, pad of paper, whatever, to each person. Include an envelope addressed to God. Have each person go apart and bit and write a letter to God. It doesn't have to be friendly, loving, or anything. Just whatever you want to say to God. Reading some examples might help people get over the fear or yelling at God or crying or anything like that. The idea is to take the time and write to God like you would write to anyone else. Have them take time, re-read it, etc. This focuses the mind to keep it from rambling and helps to point out where people are repeating themselves or only talking about themselves.
45 minutes should be sufficient for most, but a longer period would be good for some people and overnight would be perfect if it is possible.
When everyone comes back together, split up into small groups of two or three. Have each person read just a small piece of what they wrote. What made them want to say this to God? Was it painful? Was it freeing? Was it just a time of praise? What moved them to write these things? And especially, what was different about this prayer than how you normally pray?
After sharing for a time, the people then symbolically mail off their letters to God. It is important to make sure that after symbolically writing their thoughts down they symbolically send them to God. Otherwise the symbol is incomplete and leaves the wrong idea, that God will never hear these things.