The MACHO project is a search for dark matter in the form of massive compact halo objects (MACHOs). The project has photometrically monitored over forty million stars in the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), and Galactic bulge in search of rare gravitational microlensing events caused by these otherwise invisible objects. In 5.7 yr of observations toward the LMC some 13-17 microlensing events have been observed by the MACHO survey, allowing a direct estimate of the optical depth of tau = 1.2(-0.3)(+0.4) x 10(-7) to be measured. A critical component of this measurement is an accurate determination of the survey's detection efficiency. The detection efficiency is a complicated function of temporal sampling, stellar crowding (the luminosity function), image quality, photometry, time-series analysis, and criteria used to select the microlensing candidates. Here we describe the details of a Monte Carlo used to calculate the efficiency presented in the MACHO 5.7 yr LMC results. A similar calculation was performed for MACHO's 1 yr and 2 yr results. Several shortcomings of these past determinations are corrected, including the addition of fainter source stars, an up-to-date luminosity function for the LMC, and many other improvements. We find the MACHO detection efficiency peaks at 40%-50% for durations between 100 < <300 days, depending upon the selection criteria employed.