  We consider the classical evolution of the inflaton field $\phi(t)$ and the
Hubble parameter $H(t)$ in homogeneous and isotropic single-field inflation
models. Under an extremely broad assumption, we show that the universe
generically emerges from an initial singularity in a non-inflating state where
the kinetic energy of the inflaton dominates its potential energy,
$\dot{\phi}^2 \gg V(\phi)$. In this kinetically-dominated regime, the dynamical
equations admit simple analytic solutions for $\phi(t)$ and $H(t)$, which are
independent of the form of $V(\phi)$. In such models, these analytic solutions
thus provide a simple way of setting the initial conditions from which to start
the (usually numerical) integration of the coupled equations of motion for
$\phi(t)$ and $H(t)$. We illustrate this procedure by applying it to
spatially-flat models with polynomial and exponential potentials, and determine
the background evolution in each case; generically $H(t)$ and $|\phi(t)|$ as
well as their time derivatives decrease during kinetic dominance until
$\dot{\phi}^2\sim V(\phi)$, marking the onset of a brief period of fast-roll
inflation prior to a slow roll phase. We also calculate the approximate
spectrum of scalar perturbations produced in each model and show that it
exhibits a generic damping of power on large scales. This may be relevant to
the apparent low-$\ell$ falloff in the CMB power spectrum.
