The authors propose a numerical method for the uniformization of Riemann surfaces and algebraic curves in genus two with highly accurate results. Let $G$ be a Fuchsian group acting on the unit disk $Bbb D$, and let $S = Bbb D / G$. It is well known that $S$ is also in natural way an algebraic curve. The authors describe a practical way to compute, in genus 2, the uniformizing function from the unit disk to an algebraic curve. The basic idea underlying the method is to reduce the problem to the known case of genus 1. Moreover, they produce an algorithm to compute an approximation of uniformizing functions (the algorithm code and results of computations can be found at the second named author's homepage.