The basic idea behind principal component regression is to replace the predictors (i.e., individual proxies) with a smaller number of objectively determined variables that are linear combinations of the original proxies. (nap.edu)
Quadrelli and Wallace (2004) found that many patterns of NH interannual variability can be reconstructed as linear combinations of the first two Empirical Orthogonal Functions (EOFs) of sea level pressure (approximately the NAM and the PNA). (ipcc.ch)
It does touch on linear combinations, so I recommend teaching that first (also available from my shop) and looks in detail at little issues / mistakes that people can make. (tes.com)