The National Solar Observatory’s SOLIS Vector Spectromagnetograph, which will produce three or more full-disk maps of the Sun’s photospheric vector magnetic field every day for at least one solar magnetic cycle, is in the final stages of assembly. Initial observations, including cross-calibration with the current NASA/NSO spectromagnetograph (SPM), will soon be carried out at a test site in Tucson. This paper discusses data analysis techniques for reducing the raw data, calculation of line-of- sight magnetograms, and both quick-look and high-precision inference of vector fields from Stokes spectral profiles. Existing SPM algorithms, suitably modified to accommodate the cameras, scanning pattern, and polarization calibration optics for the VSM, will be used to ``clean’’ the raw data and to process line-of-sight magnetograms. A recent version of the High Altitude Observatory Milne-Eddington (HAO-ME) inversion code will be used for high-precision vector fields.