The physical mechanism driving mass ejection during a nova eruption is still poorly understood. Possibilities include ejection in a single ballistic event, a common-envelope interaction, a continuous wind, or some combination of these processes. Here, we present a study of 12 Galactic novae, for which we have premaximum high-resolution spectroscopy. All 12 novae show the same spectral evolution. Before optical peak, they show a slow P Cygni component. After peak, a fast component quickly arises, while the slow absorption remains superimposed on top of it, implying the presence of at least two physically distinct flows. For novae with high-cadence monitoring, a third, intermediate-velocity component is also observed. These observations are consistent with a scenario where the slow component is associated with the initial ejection of the accreted material and the fast component with a radiation-driven wind from the white dwarf. When these flows interact, the slow flow is swept up by the fast flow, producing the intermediate component. These colliding flows may produce the gamma-ray emission observed in some novae. Our spectra also show that the transient heavy-element absorption lines seen in some novae have the same velocity structure and evolution as the other lines in the spectrum, implying an association with the nova ejecta rather than a preexisting circumbinary reservoir of gas or material ablated from the secondary. While this basic scenario appears to qualitatively reproduce multiwavelength observations of classical novae, substantial theoretical and observational work is still needed to untangle the rich diversity of nova properties.