Spatial surface soil moisture can be an important indicator of crop conditions on farmland, but its continuous estimation remains challenging due to coarse spatial and temporal resolution of existing remotely-sensed products. Furthermore, while preceding research on soil moisture using remote sensing (surface energy balance, weather parameters, and vegetation indices) has demonstrated a relationship between these factors and soil moisture, practical continuous spatial quantification of the latter is still unavailable for use in water and agricultural management. In this study, a methodology is presented to estimate volumetric surface soil moisture by statistical selection from potential predictors that include vegetation indices and energy balance products derived from satellite (Landsat) imagery and weather data as identified in scientific literature. This methodology employs a statistical learning machine called a Relevance Vector Machine (RVM) to identify and relate the potential predictors to soil moisture by means of stratified cross-validation and forward variable selection. Surface soil moisture measurements from irrigated agricultural fields in Central Utah in the 2012 irrigation season were used, along with weather data, Landsat vegetation indices, and energy balance products. The methodology, data collection, processing, and estimation accuracy are presented and discussed.