  We present an empirical method that uses multicolor light curve shapes (MLCS)
to estimate the luminosity, distance, and total line-of-sight extinction of
Type Ia supernovae (SN Ia). The empirical correlation between the MLCS and the
luminosity is derived from a ``training set'' of nine SN Ia light curves with
independent distance and reddening estimates. We find that intrinsically dim SN
Ia are redder and have faster light curves than the bright ones which are slow
and blue. By thirty-five days after maximum the intrinsic color variations
become negligable. A formal treatment of extinction employing Bayes' theorem is
used to estimate the best value and its uncertainty. Applying MLCS to both
light curves and to color curves provides enough information to determine which
supernovae are dim because they are distant, which are intrinsically dim, and
which are dim because of extinction by dust. The precision of the MLCS
distances is examined by constructing a Hubble diagram with an independent set
of twenty SN Ia's. The dispersion of 0.12 mag indicates a typical distance
accuracy of 5 % for a single object, and the intercept yields a Hubble constant
on the Cepheid distance scale (Sandage et al 1994, 1996) of H_0=65 \pm 3
(statistical) km/s/Mpc ( \pm 6 total error). The slope of 0.2010 pm 0.0035 mag
over the distance interval 32.2 < mu < 38.3 yields the most precise
confirmation of the linearity of the Hubble law.
