The Spitzer-SDSS-GALEX Spectroscopic Survey (SSGSS) provides a new sample of 101 star-forming galaxies at z < 0.2 with unprecedented multi-wavelength coverage. New mid- to far-infrared spectroscopy from the Spitzer Space Telescope is added to a rich suite of previous imaging and spectroscopy, including ROSAT, Galaxy Evolution Explorer, Sloan Digital Sky Survey, Two Micron All Sky Survey, and Spitzer/SWIRE. Sample selection ensures an even coverage of the full range of normal galaxy properties, spanning two orders of magnitude in stellar mass, color, and dust attenuation. In this paper we present the SSGSS data set, describe the science drivers, and detail the sample selection, observations, data reduction, and quality assessment. Also in this paper, we compare the shape of the thermal continuum and the degree of silicate absorption of these typical, star-forming galaxies to those of starburst galaxies. We investigate the link between star formation rate, infrared luminosity, and total polycyclic aromatic hydrocarbon luminosity, with a view to calibrating the latter for spectral energy distribution models in photometric samples and at high redshift. Last, we take advantage of the 5-40 micron spectroscopic and far-infrared photometric coverage of this sample to perform detailed fitting of the Draine et al. dust models, and investigate the link between dust mass and star formation history and active galactic nucleus properties.