We apply recent advances in equilibrium and nonequilibrium finite-temperature field theory to the dynamics of the electroweak phase transition in the early Universe. The equation of state and the parameters that enter the nucleation rate, including the preexponential factor, are calculated in the one-loop plus ring-diagram approximation in the standard model. The velocity of bubble growth is taken from a recent relativistic kinetic theory calculation. We compute the temperature, average bubble size, bubble density, and fraction of space which has been converted from the high-temperature symmetric phase to the low-temperature asymmetric phase as functions of time. Compared to the idealized adiabatic Maxwell construction of phase equilibrium, the start of the phase transition is significantly delayed, but then completes in a much shorter time interval.