This study demonstrates how to use "spmoran", an R package estimating spatial additive mixed models and other spatial regression models for Gaussian and non-Gaussian data. Moran eigenvectors are used to an approximate Gaussian process modeling which is interpretable in terms of the Moran coefficient. The GP is used for modeling the spatial processes in residuals and regression coefficients. All these models are estimated computationally efficiently. The sample codes are available from https://github.com/dmuraka/spmoran. While this vignette mainly focuses on Gaussian regression modeling, another vignette focusing on non-Gaussian regression modeling and count regression modeling is also available from the same GitHub page.