The Submillimetre Common-User Bolometer Array (SCUBA) Half-Degree Extragalactic Survey (SHADES) is a major new blank-field extragalactic submillimetre (submm) survey currently underway at the James Clerk Maxwell Telescope (JCMT). Ultimately, SHADES aims to cover half a square degree at 450 and 850 μm to a 4σ depth of ≃ 8 mJy at 850 μm. Two fields are being observed, the Subaru/XMM–Newton Deep Field (SXDF) (02h18m− 05°) and the Lockman Hole East (10h52m+ 57°). The survey has three main aims: (i) to investigate the population of high-redshift submm galaxies and the cosmic history of massive dust-enshrouded star formation activity; (ii) to investigate the clustering properties of submm-selected galaxies in order to determine whether these objects could be progenitors of present-day massive ellipticals; and (iii) to investigate the fraction of submm-selected sources that harbour active galactic nuclei. To achieve these aims requires that the submm data be combined with co-spatial information spanning the radio-to-X-ray frequency range. Accordingly, SHADES has been designed to benefit from ultra-deep radio imaging obtained with the Very Large Array (VLA), deep mid-infrared observations from the Spitzer Space Telescope, submm mapping by the Balloon-borne Large Aperture Submillimetre Telescope (BLAST), deep near-infrared imaging with the United Kingdom Infrared Telescope, deep optical imaging with the Subaru Telescope and deep X-ray observations with the XMM–Newton observatory. It is expected that the resulting extensive multiwavelength data set will provide complete photometric redshift information accurate to as well as detailed spectral energy distributions for the vast majority of the submm-selected sources. In this paper, the first of a series on SHADES, we present an overview of the motivation for the survey, describe the SHADES survey strategy, provide a detailed description of the primary data-analysis pipeline and demonstrate the superiority of our adopted matched-filter source-extraction technique over, for example, Emerson-II style methods. We also report on the progress of the survey. As of 2004 February, 720 arcmin2 had been mapped with SCUBA (about 40 per cent of the anticipated final total area) to a median 1σ depth of 2.2 mJy per beam at 850 μm (25 mJy per beam at 450 μm), and the source-extraction routines give a source density of 650 ± 50 sources deg−2 > 3σ at 850 μm. Although uncorrected for Eddington bias, this source density is more than sufficient for providing enough sources to answer the science goals of SHADES, once half a square degree is observed. A refined reanalysis of the original 8-mJy survey Lockman hole data was carried out in order to evaluate the new data-reduction pipeline. Of the 17 most secure sources in the original sample, 12 have been reconfirmed, including 10 of the 11 for which radio identifications were previously secured.