We describe the Studying Quenching in Intermediate-z Galaxies: Gas, anguLar momentum, and Evolution (SQuIGGLE) survey of intermediate-redshift post-starburst galaxies. We leverage the large sky coverage of the Sloan Digital Sky Survey to select ~1300 recently quenched galaxies at 0.5<z<=0.9 based on their unique spectral shapes. These bright, intermediate-redshift galaxies are ideal laboratories to study the physics responsible for the rapid quenching of star formation: they are distant enough to be useful analogs for high-redshift quenching galaxies, but low enough redshift that multiwavelength follow-up observations are feasible with modest telescope investments. We use the Prospector code to infer the stellar population properties and nonparametric star formation histories (SFHs) of all galaxies in the sample. We find that SQuIGGLE galaxies are both very massive (M_*_~10^11.25^M_{sun}_) and quenched, with inferred star formation rates <~1M_{sun}_/yr, more than an order of magnitude below the star-forming main sequence. The best-fit SFHs confirm that these galaxies recently quenched a major burst of star formation: >75% of SQuIGGLE galaxies formed at least a quarter of their total stellar mass in the recent burst, which ended just ~200Myr before observation. We find that SQuIGGLE galaxies are on average younger and more burst-dominated than most other z<~1 post-starburst galaxy samples. This large sample of bright post-starburst galaxies at intermediate redshift opens a wide range of studies into the quenching process. In particular, the full SQuIGGLE survey will investigate the molecular gas reservoirs, morphologies, kinematics, resolved stellar populations, active galactic nucleus incidence, and infrared properties of this unique sample of galaxies in order to place definitive constraints on the quenching process.