We have developed a new method and the necessary numerical procedures to solve the time-dependent Schroedinger equation for an atom in intense laser fields. This method allows us to obtain not only the total ionization rate, but also the emitted photoelectron spectrum. We report nonperturbative calculations at high intensity with extensions of the method to systems including a realistic pulse shape. The influence of the resonant intermediate states is seen in the total ionization rate as well as the photoelectron spectrum, and nonlinear ac Stark shifts are found at higher intensities.