The WiggleZ Dark Energy Survey is a survey of 240000 emission-line galaxies in the distant Universe, measured with the AAOmega spectrograph on the 3.9-m Anglo-Australian Telescope (AAT). The primary aim of the survey is to precisely measure the scale of baryon acoustic oscillations (BAO) imprinted on the spatial distribution of these galaxies at look-back times of 4-8Gyr. The target galaxies are selected using ultraviolet (UV) photometry from the Galaxy Evolution Explorer satellite, with a flux limit of NUV<22.8mag. We also require that the targets are detected at optical wavelengths, specifically in the range 20.0<r<22.5mag. We use the Lyman break method applied to the UV colours, with additional optical colour limits, to select high-redshift galaxies. The galaxies generally have strong emission lines, permitting reliable redshift measurements in relatively short exposure times on the AAT. The median redshift of the galaxies is z_med_=0.6. The redshift range containing 90 per cent of the galaxies is 0.2<z<1.0. The survey will sample a volume of ~1Gpc^3^ over a projected area on the sky of 1000deg^2^, with an average target density of 350deg^-2^.