If prayer is talking to God, meditation is listening to God. This basic concept provides a starting point for growth. But meditation is just a tool, not a goal in itself.
The Relaxation Response
Meditation does not have to contain "mystical" or "spiritual" elements to be effective. As described by Benson and Klipper, anyone can gain most of the benefits of mediation by following four guidelines. The authors describe the "flight or fight" response to stress in humans and other animals and the resulting health effects. The name of the book comes from the name of a response which produces the opposite effects in humans, named the Relaxation Response.
When thinking of meditation, many will think of the Eastern techniques from the Hindu and Buddhist traditions. These typically involve sitting still or walking calmly and focusing the mind on a particular object.
The Three Pillars of Zen
One of the best introductions to zen available. Philip Kapleau was a translator for a zen master (Yasutani-roshi) in Japan in the 1950's. He translated between the master and his western students as they came in for private sessions. With the permission of master and students, excerpts of these sessions are published here. The transcripts show the students attempting to come to grips with their appointed koans and the master patiently, and at times very directly, trying to help. Some of the students struggle long and hard trying to "get it" while others have an easier time of it. The Roshi again and again points them in the right direction.
This form of meditation can involve the review of a prayer or other spiritual writing. Concentrate, re-read, try to understand the message or feeling the writer was trying to convey. We can also contemplate nature or our own conception of what God is and what God means to us.
Many "guided meditations" or visualizations have been used to help provide a pathway from the normal condition of the mind (turbulent and involved in everyday concerns and activities) to a more peaceful state.
Ken Wilber has developed a very complete overview of spiritual development based on the experience of traditions from around the world.
Wikipedia on Wilber