We describe new methods of analysis that have been developed in order to make optimal use of the stellar spectral data obtained during the course of follow-up medium-resolution observations of color-selected stars from the ``Century Survey.'' The initial selection of stars in the stellar component of the Century Survey is based on broadband V and R photometry covering a strip of 1o x 64o degrees over the range 8h5 <= R.A. <= 13h5 . We have endeavored to identify stars of spectral type A, in particular those stars which are likely to be field horizontal-branch (FHB) stars, as well as those at or near the main-sequence turnoff of the halo and thick-disk populations. Once the candidates are identified, we obtain medium-resolution spectroscopy of the sample using the FAST spectrograph on the Tillinghast 60" telescope on Mount Hopkins. These data are supplemented, where available, with JHK photometry obtained from early release 2MASS data. The spectra are analyzed with LTE model atmospheres to determine effective temperatures, metallicities, and gravities for the sample. In addition, we obtain estimates of C/Fe and Mg/Fe ratios from the strength of the CH G-band and the Mb I triplet. As the spectra are flux calibrated, we used the best-matching synthetic spectra and stellar evolutionary calculations to estimate distances to dwarfs and giants. Three different methods have been used to identify FHB stars, and to distinguish them from their higher surface gravity counterparts of similar temperature (many of which are likely to be blue stragglers). Distances to FHB stars are obtained using previously published relationships between their luminosity, temperature, and metal abundance. These data are then used to perform kinematic analyses of the sample, as described in a separate abstract.