We study finitely generated discrete groups of hyperbolic plane isometries (including those which reverse orientation) with non-compact orbit space. A presentation by generators and relations of this type of group is obtained. To that end, we use the geometrical properties of a fundamental region with a canonical form, and apply Macbeath’s classical theorem on presentations of groups of isometries of simply connected spaces. Our main result here is a complete version of a structure theorem stated without proof by Zieschang, Vogt and Coldewey in \cite{Zieschang1980}.