This dissertation investigates the coupling between the large-scale atmospheric circulation and surface processes on Titan, with a particular focus on methane precipitation and its influence on surface geomorphology and hydrology. As the only body in the Solar System with an active hydrologic cycle other than Earth, Titan presents a valuable laboratory for studying principles of hydroclimate on terrestrial planets. Idealized general circulation models (GCMs) are used here to test hypotheses regarding Titan's surface-atmosphere connections. First, an Earth-like GCM simulated over a range of rotation rates is used to evaluate the effect of rotation rate on seasonal monsoon behavior. Slower rotation rates result in poleward migration of summer rain, indicating a large-scale atmospheric control on Titan's observed dichotomy of dry low latitudes and moist high latitudes. Second, a Titan GCM benchmarked against observations is used to analyze the magnitudes and frequencies of extreme methane rainstorms as simulated by the model. Regional patterns in these extreme events correlate well with observed geomorphic features, with the most extreme rainstorms occurring in mid-latitude regions associated with high alluvial fan concentrations. Finally, a planetary surface hydrology scheme is developed and incorporated into a Titan GCM to evaluate the roles of surface flow, subsurface flow, infiltration, and groundmethane evaporation in Titan's climate. The model reproduces Titan's observed surface liquid and cloud distributions, and reaches an equilibrium state with limited interhemispheric transport where atmospheric transport is approximately balanced by subsurface transport. The equilibrium state suggests that Titan's current hemispheric surface liquid asymmetry, favoring methane accumulation in the north, is stable in the modern climate.