Abstract: Preliminary observations and computational methods for analysis are presented for observing celestial objects with time-varying intensity, in particular transiting exoplanets. Transits occur when a planet orbiting a star other than the sun (an exoplanet) passes between the Earth and the host star, slightly dimming the apparent intensity of the star. CCD images of the host star of one such exoplanet, HD 189733b, are recorded during predicted transits at the University of Maryland Observatory (UMO) on a small (152 mm) refracting telescope. Differential photometry algorithms compare the relative brightness of the host star to other nearby, non-variable stars in the field and detect the small change in brightness associated with a planetary transit, on the order of tens of millimagnitudes. The first successful exoplanet observations at UMO are presented and discussed, as well as possible implications for exoplanetary studies conducted by amateur and small observatories.