The MiMeS (Magnetism in Massive Stars) project is a large-scale, high-resolution, sensitive spectropolarimetric investigation of the magnetic properties of O- and early B-type stars. Initiated in 2008 and completed in 2013, the project was supported by three Large Program allocations, as well as various programmes initiated by independent principal investigators, and archival resources. Ultimately, over 4800 circularly polarized spectra of 560 O and B stars were collected with the instruments ESPaDOnS (Echelle SpectroPolarimetric Device for the Observation of Stars) at the Canada-France-Hawaii Telescope, Narval at the Telescope Bernard Lyot and HARPSpol at the European Southern Observatory La Silla 3.6m telescope, making MiMeS by far the largest systematic investigation of massive star magnetism ever undertaken. In this paper, the first in a series reporting the general results of the survey, we introduce the scientific motivation and goals, describe the sample of targets, review the instrumentation and observational techniques used, explain the exposure time calculation designed to provide sensitivity to surface dipole fields above approximately 100G, discuss the polarimetric performance, stability and uncertainty of the instrumentation, and summarize the previous and forthcoming publications.