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We describe the survey design, calibration, commissioning, and emission-line detection algorithms for the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX). The goal of HETDEX is to measure the redshifts of over a million Lyαemitting galaxies between 1.88 <z< 3.52, in a 540 deg²area encompassing a comoving volume of 10.9 Gpc³. No preselection of targets is involved; instead the HETDEX measurements are accomplished via a spectroscopic survey using a suite of wide-field integral field units distributed over the focal plane of the telescope. This survey measures the Hubble expansion parameter and angular diameter distance, with a final expected accuracy of better than 1%. We detail the project’s observational strategy, reduction pipeline, source detection, and catalog generation, and present initial results for science verification in the Cosmological Evolution Survey, Extended Groth Strip, and Great Observatories Origins Deep Survey North fields. We demonstrate that our data reach the required specifications in throughput, astrometric accuracy, flux limit, and object detection, with the end products being a catalog of emission-line sources, their object classifications, and flux-calibrated spectra.