NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. We describe the design, implementation, and initial scientific results of a system for analyzing the Digitized Second Palomar Observatory Sky Survey (DPOSS). The system (SKICAT) facilitates and largely automates the pipeline processing of DPOSS from raw pixel data into calibrated, classified object catalog form. A fundamental constraint limiting the scientific usefulness of optical imaging surveys is the level at which objects may be reliably distinguished as stars, galaxies, or artifacts. We therefore expended great effort to explore techniques that would make most efficient use of the data for classification purposes. The classifier implemented within SKICAT was created using a new machine learning technology, whereby an algorithm determines a near-optimal set of classification rules based upon training examples. Using this approach, we were able to construct a classifier which distinguishes objects to the same level of accuracy as in previous surveys using comparable plate material, but nearly one magnitude fainter (or an equivalent [...]). Our first analysis of DPOSS using SICAT is of an overlapping set of four survey fields near the North Galactic Pole, in both the J and F passbands. Through detailed simulations of a subset of these data, we were able to analyze systematic aspects of our detection and measurement procedures, as well as optimize them. We discuss how we calibrate the plate magnitudes to the Gunn-Thuan g and r photometric system using CCD sequences obtained in a program devoted expressly to calibrating DPOSS. Our technique results in an estimated plate-to-plate zero point standard error of under [...] in g and below [...] in r, for J and F plates, respectively. Using the catalogs derived from these fields, we compare our differential galaxy counts in g and r with those from recent Schmidt plate surveys as well as predictions from evolutionary and non-evolutionary (NE) galaxy models. While we find some significant differences between our measurements and others, particularly at the bright end, we find generally good agreement between our counts and recent NE and mild evolutionary models calibrated to consistently fit bright and faint galaxy counts, colors, and redshift distributions. The consistency of our results with these predictions provides additional support to the view that very recent (z < 0.1) or exotic galaxy evolution, or some non-standard forms of cosmology, may not be necessary to reconcile these diverse observations with theory.