We have observed an area of ≈27 deg2 to an rms noise level of 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 (≳0.2 deg2) 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., the first results from the 10C survey, including the deep 15.7‐GHz source count, are presented.