We present high-resolution X-ray spectra from the young supernova remnant Cas A using a 70 ks observation taken by the Chandra High Energy Transmission Grating Spectrometer (HETGS). Line emission, dominated by Si and S ions, is used for high-resolution spectral analysis of many bright, narrow regions of Cas A to examine their kinematics and plasma state. These data allow a three-dimensional (3D) reconstruction using the unprecedented X-ray kinematic results: we derive unambiguous Doppler shifts for these selected regions, with values ranging between -2500 and +4000 km s^-1 and the typical velocity error less than 200 km s^-1. Plasma diagnostics of these regions, derived from line ratios of resolved He-like triplet lines and H-like lines of Si, indicate temperatures largely around 1 keV, which we model as O-rich reverse-shocked ejecta. The ionization age also does not vary considerably over these regions of the remnant. The gratings analysis was complemented by the nondispersed spectra from the same data set, which provided information on emission measure and elemental abundances for the selected Cas A regions. The derived electron density of X-ray emitting ejecta varies from 20 to 200 cm^-3. The measured abundances of Mg, Si, S, and Ca are consistent with O being the dominant element in the Cas A plasma. With a diameter of 5', Cas A is the largest source observed with the HETGS to date. We therefore describe the technique we use and some of the challenges we face in the HETGS data reduction from such an extended, complex object.