We present an updated version of the multicolor light-curve shape method to measure distances to Type Ia supernovae (SNe Ia), incorporating new procedures for K-correction and extinction corrections. We also develop a simple model to disentangle intrinsic color variations and reddening by dust and expand the method to incorporate U-band light curves and to more easily accommodate prior constraints on any of the model parameters. We apply this method to 133 nearby SNe Ia, including 95 objects in the Hubble flow (cz>=2500km/s), which give an intrinsic dispersion of less than 7% in distance. The Hubble flow sample, which is of critical importance to all cosmological uses of SNe Ia, is the largest ever presented with homogeneous distances.