The long term distribution of random dynamical systems or systems which are driven by external influences can be difficult to estimate by simulation of long orbits. For deterministic systems, Ulam's method has been used successfully to provide a superior method of estimating long term distributions or natural invariant measures. In this note, we describe the extension of Ulam's method random and forced systems. These extensions automatically filter out the inherent randomness and ``non-stationarity'' contained in simulated orbits.