We present a succinct yet self-contained treatment of the Dual Mesh Control Domain Method, a novel numerical technique that hybridizes the finite element and finite volume methods. The theoretical aswell as implementation aspects of this method are addressed, and its applications to the linear and nonlinear (in the von Kármán sense) bending analysis of functionally graded beams and orthotropic plates are demonstrated. While the chapter is intended for a broad audience, including readers new to numerical methods, it is specifically devoted to those interested in implementing the Dual Mesh Control Domain Method. To that end, computational aspects related to assembly, generation of shape functions and their derivatives, numerical integration, and solution techniques for nonlinear systems of equations are discussed in reasonable depth. Additionally, examples replete with numerical data and plots are provided to assist interested readers in reproducing and extending the presented results. Although the emphasis of the chapter leans toward structural applications, the method has also been successfully applied to problems in heat transfer and fluid mechanics, making it valuable to anyone seeking to learn and adopt this novel and versatile numerical technique.