  The Red-Sequence Cluster Survey (RCS) is a $\sim$100 square degree,
two-filter imaging survey in the $R_C$ and $z'$ filters, designed primarily to
locate and characterise galaxy clusters to redshifts as high as $z=1.4$. This
paper provides a detailed description of the survey strategy and execution,
including a thorough discussion of the photometric and astrometric calibration
of the survey data. The data are shown to be calibrated to a typical
photometric uncertainty of 0.03-0.05 magnitudes, with total astrometric
uncertainties less than 0.25 arcseconds for most objects. We also provide a
detailed discussion of the adaptation of a previously described cluster search
algorithm (the cluster red-sequence method) to the vagaries of real survey
data, with particular attention to techniques for accounting for subtle
variations in survey depths caused by changes in seeing and sky brightness and
transparency. A first catalog of RCS clusters is also presented, for the survey
patches RCS0926+37 and RCS1327+29. These catalogs, representing about 10% of
the total survey and comprising a total of 429 candidate clusters and groups,
contain a total of 67 cluster candidates at a photometric redshift of
$0.9<z<1.4$, down to the chosen significance threshold of 3.29$\sigma$.
