The XMM Cluster Survey (XCS) is a serendipitous search for galaxy clusters using all publicly available data in the XMM-Newton Science Archive. Its main aims are to measure cosmological parameters and trace the evolution of X-ray scaling relations. In this paper we describe the data processing methodology applied to the 5,776 XMM observations used to construct the current XCS source catalogue. A total of 3,675 > 4-sigma cluster candidates with > 50 background-subtracted X-ray counts are extracted from a total non-overlapping area suitable for cluster searching of 410 deg^2. Of these, 993 candidates are detected with > 300 background-subtracted X-ray photon counts, and we demonstrate that robust temperature measurements can be obtained down to this count limit. We describe in detail the automated pipelines used to perform the spectral and surface brightness fitting for these candidates, as well as to estimate redshifts from the X-ray data alone. A total of 587 (122) X-ray temperatures to a typical accuracy of < 40 (< 10) per cent have been measured to date. We also present the methodology adopted for determining the selection function of the survey, and show that the extended source detection algorithm is robust to a range of cluster morphologies by inserting mock clusters derived from hydrodynamical simulations into real XMM images. These tests show that the simple isothermal beta-profiles is sufficient to capture the essential details of the cluster population detected in the archival XMM observations. The redshift follow-up of the XCS cluster sample is presented in a companion paper, together with a first data release of 503 optically-confirmed clusters.
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