(Abridged) We discuss the design considerations of the EXPLORE (EXtra-solar PLanet Occultation REsearch) project, a series of transiting planet searches using 4-m-class telescopes to continuously monitor a single field of stars in the Galactic Plane in each ~2 week observing campaign. We discuss the general factors which determine the efficiency and the number of planets found by a transit search, including time sampling strategy and field selection. The primary goal is to select the most promising planet candidates for radial velocity follow-up observations. We show that with very high photometric precision light curves that have frequent time sampling and at least two detected transits, it is possible to uniquely solve for the main parameters of the eclipsing system (including planet radius) based on several important assumptions about the central star. Together with a measured spectral type for the star, this unique solution for orbital parameters provides a powerful method for ruling out most contaminants to transiting planet candidates. For the EXPLORE project, radial velocity follow-up observations for companion mass determination of the best candidates are done on 8-m-class telescopes within two or three months of the photometric campaigns. This same-season follow-up is made possible by the use of efficient pipelines to produce high quality light curves within weeks of the observations. We conclude by presenting early results from our first search, EXPLORE I, in which we reached <1% rms photometric precision (measured over a full night) on ~37,000 stars to I <= 18.2.