American Scientst has a nice article by Brian Hayes recounting the basic physics of climate, and then recommending both public engagement with clear, simple climate models, at least by the curious and scientifically literate, and the development of models which can be thus understood. He goes on to offer a number of resources offering such models. This is great.
However, this is both hardly a new phenomenon, especially with Python, and it doesn’t relieve the curious student of climate from the public of knowing some of the physics contributing to these calculations. Toward that end I would recommend the course by Professor David Archer, accompanying textbook, video lectures, and computer codes, and my favorite textbook by Professor Ray Pierrehumbert (Principles of Planetary Climate), with data and Python code, allowing the student to not only understand details of these physics, but see them through a graded series of models and calculations.
NOAA also has a number of Web pages devoted to climate and weather data: