We study the transition from fluid at rest to turbulence in a rotating tank. The energy is transported by inertial wave packets through the fluid volume. These high amplitude waves propagate at velocities consistent with those calculated from linearized theory. A "front" in the temporal evolution of the energy power spectrum indicates a time scale for energy transport at the linear wave speed. Nonlinear energy transfer between modes is governed by a different, longer, time scale. The observed mechanisms can lead to significant differences between rotating and two-dimensional turbulent flows.