Instead of looking for 'problems' and 'needs', Appreciative Inquiry is an approach that builds on existing strengths and resources of an organisation or a community. It turns 'needs assessment' on its head.
Joe Hall and Sue Hammond provide a basic introduction to Appreciative Inquiry and give an example of it in practice in What is Appreciative Inquiry? (Adobe PDF, 9 pages, 34 KB). Sue Hammond is also the author of The Thin Book of Appreciative Inquiry
A comprehensive website sharing resources and tools on this topic is the Appreciative Inquiry Commons. It includes particular sections on using Appreciative Inquiry with non-profits and NGOs and resources for the 'community sector'.
A good book for anyone interested in using Appreciative Inquiry is the Appreciative Inquiry Handbook by David Cooperrider, Diana Whitney and Jacqueline Stavros. It includes a CD with many templates and examples as well as 'how to' guides. (David Cooperrider of Case Western Reserve University is the original developer of Appreciative Inquiry.)
The Appreciative Inquiry approach in communities is sometimes called Asset-Based Community Development (ABCD). Here it is based on community action research by John McKnight and John Kretzmann.
A very useful collection of ABCD resources and links is the ABCD Institute at Northwestern University. McKnight and Kretzmann's book Building Communities from the Inside Out: A Path Toward Finding and Mobilizing a Community's Assets outlines in simple, "neighbourhood-friendly" terms what local communities can do to start their own journey down the path of asset-based development.