Bubba provides a very good overview of a standard general circulation model. There are an almost limitless number of variations as the models themselves can be tweaked to focus in on specific aspects, to include or exclude any number of variables, to assign different weightings, interactions, feedbacks, probabilities etc.
In essence you can think of a model as being a computer simulation. Information is fed into it about lots of different factors that affect the climate and the model is then run. The result is a forecast of what the future climate could be like.
One of the problems you’re going to face in explaining GCM’s is that, whilst he concept is simple, the workings are phenomenally complicated, that’s why they need some of the world’s most powerful computers to run them. Some of the links below provide summaries and if you experiment with the NCAR model (one you can download and use yourself) it may help put things into perspective.
The same links should also address the points you were told to answer. But to provide a satisfactory answer that meets the specified criteria you’re going to have to learn something about the models – and that’s not going to be all that easy.
To get you started, a typical model will factors in many variables. The way the variables act and react can be changed, so too can the way the influence each other and the way they interact together. A basic climate model will include the following:
• The land↔atmosphere interaction
• The soil↔biosphere interaction
• The atmosphere↔biosphere interaction
• The ice↔ocean interaction
• The atmpsphere↔ice interaction
• Cryospherics: Glaciers, ice sheets, ice shelves, sea-ice, snow, permafrost, frozen ground etc
• Land surfaces: Vegetation, geomorphology, ecosystems, land use, land use change, albedo, volcanoes
• Oceanics: Biogeochemistry, thermohaline and other circulations, sea-levels
• Hydrology: Evapouration, transpiration, precipitation, cloud cover
• Weather: Wind stresses, wind dynamics, thermodynamics
• Oscillations in the oceans and atmosphere. Very long term models will take planetary oscillations into account.
• Radiation: Terrestrial and solar, changes to both
• Boundary transitions
• Changes in solar activity
• Changes in human activity
More info…
The NCAR Single-column Community Climate Model
http://www.cgd.ucar.edu/cms/sccm/sccm.html
Climate Models: An Assessment of Strengths and Limitations
http://www.clivar.org/organization/wgcm/references/sap3-climate-models.pdf
The JASON’s climate model of the world (the first real climate model)
http://www.nap.edu/catalog.php?record_id=12181
IPCC Model Outputs
http://www.ipcc-data.org/ar4/gcm_data.html
Climate Models and Their Evaluation
http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter8.pdf