In this paper, we describe a simple set of "recipes" for the analysis of high spatial density EEG. We focus on a linear integration of multiple channels for extracting individual components without making any spatial or anatomical modeling assumptions, instead requiring particular statistical properties such as maximum difference, maximum power, or statistical independence. We demonstrate how corresponding algorithms, for example, linear discriminant analysis, principal component analysis and independent component analysis, can be used to remove eye-motion artifacts, extract strong evoked responses, and decompose temporally overlapping components. The general approach is shown to be consistent with the underlying physics of EEG, which specifies a linear mixing model of the underlying neural and non-neural current sources.