Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the minimization of an action functional, which in many cases of interest has to be computed by numerical means. Here, a numerical method is presented to effectively compute minimizers of the Freidlin-Wentzell action functional in very general settings. The matlab source code of the algorithm and some test problems is available for download.