Supernovae are essential to understanding the chemical evolution of the Universe. Type Ia supernovae also provide the most powerful observational tool currently available for studying the expansion history of the Universe and the nature of dark energy. Our basic knowledge of supernovae comes from the study of their photometric and spectroscopic properties. However, the presently available data sets of optical and near-infrared light curves of supernovae are rather small and/or heterogeneous, and employ photometric systems that are poorly characterized. Similarly, there are relatively few supernovae whose spectral evolution has been well sampled, both in wavelength and phase, with precise spectrophotometric observations. The low-redshift portion of the Carnegie Supernova Project (CSP) seeks to remedy this situation by providing photometry and spectrophotometry of a large sample of supernovae taken on telescope/filter/detector systems that are well understood and well characterized. During a five-year program which began in September 2004, we expect to obtain high-precision ugriBVYJHKs light curves and optical spectrophotometry for about 250 supernovae of all types. In this paper we provide a detailed description of the CSP survey observing and data reduction methodology. In addition, we present preliminary photometry and spectra obtained for a few representative supernovae during the first observing campaign.