We present an improved version of FIT3D, a fitting tool for the analysis of the spectroscopic properties of the stellar populations and the ionized gas derived from moderate resolution spectra of galaxies. FIT3D is a tool developed to analyze Integral Field Spectroscopy data and it is the basis of Pipe3D, a pipeline already used in the analysis of datasets like CALIFA, MaNGA, and SAMI. We describe the philosophy behind the fitting procedure, and in detail each of the different steps in the analysis. We present an extensive set of simulations in order to estimate the precision and accuracy of the derived parameters for the stellar populations. In summary, we find that using different stellar population templates we reproduce the mean properties of the stellar population (age, metallicity, and dust attenuation) within ~0.1 dex. A similar approach is adopted for the ionized gas, where a set of simulated emission- line systems was created. Finally, we compare the results of the analysis using FIT3D with those provided by other widely used packages for the analysis of the stellar population (Starlight, Steckmap, and analysis based on stellar indices) using real high S/N data. In general we find that the parameters for the stellar populations derived by FIT3D are fully compatible with those derived using these other tools.
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