The Near-Infrared S0 Survey (NIRS0S; Laurikainen, Salo, and Buta 2005, MNRAS, 362, 1319) is an attempt to obtain a statistically well-defined database of images of S0s from which the properties of S0 bars may be fairly compared to those of spirals. The main goal of the survey is to provide information on the the distribution of bar strengths in S0 galaxies, derived using a recently developed gravitational torque indicator (Buta and Block 2001, ApJ, 550, 243; Laurikainen et al. 2004, MNRAS, 355, 1251). S0 bars, and their strengths, have not been studied in much detail before, even though these bars contain important `fossilized' information about the evolutionary history of S0 galaxies, particularly about the evolutionary connection, if any, between spirals and S0s. Previous studies have focussed more on basic properties of S0s, such as thick and thin disks, bulge-to-disk ratios, luminosities, star formation history, gas content, and environment. The Ohio State University Bright Galaxy Survey (Eskridge et al. 2002, ApJS, 143, 73) provides a valuable dataset for studying the properties of spiral galaxies, and has been used to show that the distribution of bar strengths in spirals is an approximately exponentially declining function of bar strength (Buta et al. 2005, AJ, 130, 506). The questions we ask are: (1) how strong do S0 bars get compared to spiral bars? (2) how does the distribution of bar strengths in S0 galaxies compare with that for spirals? and (3) what characterizes the morphology of bars in S0 galaxies? In this paper, we describe the rationale for the survey, its status, and present results of 2D bulge/disk/bar decompositions and of detailed analysis of the relative Fourier intensity amplitudes that characterize early-type galaxy bars. Our main findings are that, when bars are fitted simultaneously with bulges and disks, bulge-to-total luminosity ratios of S0s at 2.2 μ m come out much less (0.24 vs. 0.6) than previously thought, and that relative Fourier intensity profiles, Im/I_o (m=integer) versus radius, of bars may be described by one or more gaussian components. We also confirm the approximate validity of the symmetry assumption of Im/I_0 profiles when used in bar-spiral separation analyses (Buta, Block, and Knapen 2003, AJ, 126, 1148). This work was supported by NSF Grants AST-0205143 and AST-0507140 to the University of Alabama. Funding for the OSU Bright Galaxy Survey was provided by NSF grants AST-9217716 and AST-9617006, with additional funding from the Ohio State University.