The care group model starts with the health and wellness of the church's own members. The idea is that as people share together in meaningful but safe ways about their history and life experience, those issues that impact a person's overall well-being will be heard and addressed. Some congregations see the mutual support approach as a way of laying a foundation for further programs around health and wellness. Others see it as an end in itself. Often it's a place to start and things emerge from it that you can't even imagine at the outset.
People sharing their stories and exploring the implications for their lives is powerful.
The important thing is to design something that will work well in your context and to be responsive to the unexpected. There are several programs that are ready to use that outline a way to organize care groups. These programs can be used flexibly or can be adapted to suit the needs of your congregation. The Advocate Community Ministry Resource Library holds some of these materials. The Church of the Brethren's Association of Brethren Caregivers has an excellent program called Lafiya, from the Nigerian word meaning to be well or whole.