  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
Ly$\alpha$ emitting galaxies between 1.88<z<3.52, in a 540 deg^2 area
encompassing a co-moving volume of 10.9 Gpc^3. No pre-selection 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 COSMOS, Extended Groth Strip, and GOODS-N
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.
