Let X(F, G) be the G-character variety of F where G is a rank 1 complex affine algebraic group and F is a finitely presentable discrete group. We describe an algorithm, which we implement in Mathematica, that takes a finite presentation for F and produces a finite presentation of the coordinate ring of X(F,G). The main results in this paper are not new, although we hope that as a well-referenced exposition with a companion computer program, it will be useful.