We describe the development and implementation of the Sloan Extension for Galactic Exploration and Understanding (SEGUE) Stellar Parameter Pipeline (SSPP). The SSPP is derived, using multiple techniques, radial velocities, and the fundamental stellar atmospheric parameters (effective temperature, surface gravity, and metallicity) for AFGK-type stars, based on medium-resolution spectroscopy and ugriz photometry obtained during the course of the original Sloan Digital Sky Survey (SDSS-I) and its Galactic extension (SDSS-II/SEGUE). The SSPP also provides spectral classification for a much wider range of stars, including stars with temperatures outside the window where atmospheric parameters can be estimated with the current approaches. This is Paper I in a series of papers on the SSPP; it provides an overview of the SSPP, and tests of its performance using several external data sets. Random and systematic errors are critically examined for the current version of the SSPP, which has been used for the sixth public data release of the SDSS (DR-6).