I recomend that people read (upto and including section 5.3 (13 pages) of) the paper "Predction with Gaussian Processes: from linear regression to linear prediction and beyond" by Chris Williams. It appears in the book "Learning and Inference in graphical Models",

M. I. Jordan, Kluwer Academic Press, 1998; and can be found online at

http://www.ncrg.aston.ac.uk/Papers/postscript/NCRG_97_012.ps.Z

Another good review paper (for the exceptionally eager) may be found at David MacKay's web page: "Gaussian Processes - a replacement for Supervised Neural Networks?"

http://wol.ra.phy.cam.ac.uk/mackay/gp.ps.gz