  We describe a method for measuring the integrated Comptonization (YSZ) of
clusters of galaxies from measurements of the Sunyaev-Zel'dovich (SZ) effect in
multiple frequency bands and use this method to characterize a sample of galaxy
clusters detected in South Pole Telescope (SPT) data. We test this method on
simulated cluster observations and verify that it can accurately recover
cluster parameters with negligible bias. In realistic simulations of an
SPT-like survey, with realizations of cosmic microwave background anisotropy,
point sources, and atmosphere and instrumental noise at typical SPT-SZ survey
levels, we find that YSZ is most accurately determined in an aperture
comparable to the SPT beam size. We demonstrate the utility of this method to
measure YSZ and to constrain mass scaling relations using X-ray mass estimates
for a sample of 18 galaxy clusters from the SPT-SZ survey. Measuring YSZ within
a 0.75' radius aperture, we find an intrinsic log-normal scatter of 21+/-11% in
YSZ at a fixed mass. Measuring YSZ within a 0.3 Mpc projected radius
(equivalent to 0.75' at the survey median redshift z = 0.6), we find a scatter
of 26+/-9%. Prior to this study, the SPT observable found to have the lowest
scatter with mass was cluster detection significance. We demonstrate, from both
simulations and SPT observed clusters, that YSZ measured within an aperture
comparable to the SPT beam size is equivalent, in terms of scatter with cluster
mass, to SPT cluster detection significance.
