  We have measured the parity-violating electroweak asymmetry in the elastic
scattering of polarized electrons from protons. Significant contributions to
this asymmetry could arise from the contributions of strange form factors in
the nucleon. The measured asymmetry is $A = -15.05 \pm 0.98 ({\rm stat}) \pm
0.56 ({\rm syst})$ ppm at the kinematic point $<\theta_{\rm lab} > =
12.{3^\circ} $ and $<Q^2 > = 0.477$ (GeV/c)$^2$. Based on these data as well as
data on electromagnetic form factors, we extract the linear combination of
strange form factors $G^s_E + 0.392 G^s_M = 0.014 \pm 0.020 \pm 0.010$ where
the first error arises from this experiment and the second arises from the
electromagnetic form factor data. This paper provides a full description of the
special experimental techniques employed for precisely measuring the small
asymmetry, including the first use of a strained GaAs crystal and a
laser-Compton polarimeter in a fixed target parity-violation experiment.
