Despite the complexity of convection, clouds, and precipitation, climate models robustly predict simple responses of global precipitation to greenhouse warming. In transient climates, when global climate has not yet equilibrated to changes in radiative forcing, that response can be decomposed into two components, a "fast" suppression of precipitation that is linear with changes in CO2, and a "slow" linear increase with global temperature. Both responses have characteristic regional signatures, but complex local responses nevertheless aggregate to simple global-mean behavior. We use both a fully coupled general circulation model (GCM) and a simple one-column model to show that global precipitation responses are well explained by the constraints of energy balance at the Earth's surface. The surface energy budget framework is not inconsistent with previous explanations, but allows a simpler understanding of relevant processes. Because the single-column model captures global-mean behavior in full GCMs, it allows detailed exploration of those processes. Increased precipitation with temperature (the "slow" response) is driven largely by enhanced IR absorption by atmospheric water vapor, which inhibits radiative cooling from the surface. Initial precipitation suppression in transient climates after addition of CO2 (the "fast" response) occurs because the atmosphere adjusts until latent heat export is reduced to compensate for ocean heat uptake. However, while global behavior is reproducible by simple models, the regional pattern of the transient precipitation response remains an outstanding research problem.