Given that low-mass stars have intrinsically low luminosities at optical wavelengths and a propensity for stellar activity, it is advantageous for radial velocity (RV) surveys of these objects to use near-infrared (NIR) wavelengths. In this work we describe and test a novel RV extraction pipeline dedicated to retrieving RVs from low mass stars using NIR spectra taken by the CSHELL spectrograph at the NASA Infrared Telescope Facility, where a methane isotopologue gas cell is used for wavelength calibration. The pipeline minimizes the residuals between the observations and a spectral model composed of templates for the target star, the gas cell, and atmospheric telluric absorption; models of the line spread function, continuum curvature, and sinusoidal fringing; and a parameterization of the wavelength solution. The stellar template is derived iteratively from the science observations themselves without a need for separate observations dedicated to retrieving it. Despite limitations from CSHELL's narrow wavelength range and instrumental systematics, we are able to (1) obtain an RV precision of 35 m/s for the RV standard star GJ 15 A over a time baseline of 817 days, reaching the photon noise limit for our attained SNR, (2) achieve ~3 m/s RV precision for the M giant SV Peg over a baseline of several days and confirm its long-term RV trend due to stellar pulsations, as well as obtain nightly noise floors of ~2 - 6 m/s, and (3) show that our data are consistent with the known masses, periods, and orbital eccentricities of the two most massive planets orbiting GJ 876. Future applications of our pipeline to RV surveys using the next generation of NIR spectrographs, such as iSHELL, will enable the potential detection of Super-Earths and Mini-Neptunes in the habitable zones of M dwarfs.