We present K-band spectra for 133 nearby (d < 33 ps) M dwarfs, including 18 M dwarfs with reliable metallicity estimates (as inferred from an FGK type companion), 11 M dwarf planet hosts, more than 2/3 of the M dwarfs in the northern 8 pc sample, and several M dwarfs from the LSPM catalog. From these spectra, we measure equivalent widths of the Ca and Na lines, and a spectral index quantifying the absorption due to H sub(2)O opacity (the H sub(2)O-K2 index). Using empirical spectral type standards and synthetic models, we calibrate the H sub(2)O-K2 index as an indicator of an M dwarf's spectral type and effective temperature. We also present a revised relationship that estimates the Fe/H and M/H metallicities of M dwarfs from their Na I, Ca I, and H sub(2)O-K2 measurements. Comparisons to model atmosphere provide a qualitative validation of our approach, but also reveal an overall offset between the atomic line strengths predicted by models as compared to actual observations. Our metallicity estimates also reproduce expected correlations with Galactic space motions and H alpha emission line strengths, and return statistically identical metallicities for M dwarfs within a common multiple system. Finally, we find systematic residuals between our H sub(2)O-based spectral types and those derived from optical spectral features with previously known sensitivity to stellar metallicity, such as TiO, and identify the CaH1 index as a promising optical index for diagnosing the metallicities of near-solar M dwarfs.