  We have observed an area of approximatley 27 deg^2 to an rms noise level of
less than 0.2 mJy at 15.7 GHz, using the Arcminute Microkelvin Imager Large
Array. These observations constitute the most sensitive radio-source survey of
any extent (greater than approximately 0.2 deg^2) above 1.4 GHz. This paper
presents the techniques employed for observing, mapping and source extraction.
We have used a systematic procedure for extracting information and producing
source catalogues, from maps with varying noise and uv-coverage. We have
performed simulations to test our mapping and source-extraction procedures, and
developed methods for identifying extended, overlapping and spurious sources in
noisy images. In an accompanying paper, AMI Consortium: Davies et al. 2010, the
first results from the 10C survey, including the deep 15.7-GHz source count,
are presented.
