We present design considerations for a ground-based survey for transiting exoplanets around L and T dwarfs, spectral classes that have yet to be thoroughly probed for planets. We simulate photometry for L and T targets with a variety of red-optical and near-infrared (NIR) detectors, and compare the scatter in the photometry to anticipated transit depths. Based on these results, we recommend the use of a low-dark-current detector with H-band NIR photometric capabilities. We then investigate the potential for performing a survey for Earth-sized planets for a variety of telescope sizes. We simulate planetary systems around a set of spectroscopically confirmed L and T dwarfs using measured M dwarf planet occurrence rates from Kepler, and simulate their observation in surveys ranging in duration from 120 to 600 nights, randomly discarding 30% of nights to simulate weather losses. We find that an efficient survey design uses a 2 m class telescope with a NIR instrument and 360-480 observing nights, observing multiple L and T targets each night with a dithering strategy. Surveys conducted in such a manner have over an 80% chance of detecting at least one planet, and detect around 2 planets, on average. The number of expected detections depends on the true planet occurrence rate, however, which may in fact be higher for L and T dwarfs than for M dwarfs.