As part of the McDonald Observatory M dwarf planet search program, we present the results and detection limits for our high-precision radial velocity survey of 99 M dwarf stars. We also detail our efforts to improve the precision of our RV measurements as well as our frequency analysis methods. For any RV program, it is essential to obtain as high a precision as possible; increasing sensitivity can realistically reveal terrestrial-mass planets with our data. M dwarfs provide a unique opportunity to study these lower-mass planets (the so-called "super-Earths") from ground-based facilities; such planets are mostly undetectable around FGK stars, whose larger masses result in much smaller RV amplitudes. However, the low intrinsic luminosities of the M spectral type make it difficult to obtain high S/N measurements for a statistically significant sample, making our analysis improvements especially critical. Finally, we conduct a statistical analysis of the 21 known M dwarf planets. In particular, we use the photometric metallicity calibration for M dwarfs described in Johnson and Apps (2009) to further explore the frequency of planetary systems as a function of stellar metallicity. Our analysis confirms the correlation between stellar mass and the presence of giant planets, but also reveals a significant metallicity dependence on the presence of high-mass planets for M dwarfs. We show that the metallicities of our target sample are evenly distributed around solar [M/H], eliminating the possibility that the results of our survey will be biased due to metallicity effects. The frequency and characteristics of planets around M stars provides important insight into planet formation theories, especially for giant planets, which appear to form less easily around low-mass primaries. While previous results suggesting a dearth of short-period Jovian planets around M stars still holds, there is now a long enough observational time baseline to begin to characterize the frequency of planets with lower masses and larger orbital separations around these stars as opposed to other main sequence stars. / text