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We describe the survey design, calibration, commissioning, and emission-linedetection algorithms for the Hobby-Eberly Telescope Dark Energy Experiment(HETDEX). The goal of HETDEX is to measure the redshifts of over a millionLy$\alpha$ emitting galaxies between 1.88<z<3.52, in a 540 deg^2 areaencompassing a co-moving volume of 10.9 Gpc^3. No pre-selection of targets isinvolved; instead the HETDEX measurements are accomplished via a spectroscopicsurvey using a suite of wide-field integral field units distributed over thefocal plane of the telescope. This survey measures the Hubble expansionparameter and angular diameter distance, with a final expected accuracy ofbetter than 1%. We detail the project's observational strategy, reductionpipeline, source detection, and catalog generation, and present initial resultsfor science verification in the COSMOS, Extended Groth Strip, and GOODS-Nfields. We demonstrate that our data reach the required specifications inthroughput, astrometric accuracy, flux limit, and object detection, with theend products being a catalog of emission-line sources, their objectclassifications, and flux-calibrated spectra.

The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Survey Design, Reductions, and Detections