We introduce the theoretical methods which we use in this thesis. First, we introduce the variational method to obtain the ground state. While this method introduces some computational bias since it incorporates a small set of parameters that effectively describe the spin structure, it allows for efficient determination of the ground state if appropriate parameters are chosen. Next, we present a numerical optimization technique that deterministically updates the spin structure toward lower energy states. By employing an algorithm based on Adam, stable spin configurations can be efficiently obtained. Next, we present an approach to extracting parameters characterizing the superposed waves in spin moirés from numerical data generated by real-space simulations. Then, we introduce the Landau-Lifshitz-Gilbert (LLG) equation, describing the time evolution of magnetic moments. This equation allows us to analyze the real-space and real-time response of spin moirés to external fields. Then, we present a numerical method based on the linear spin-wave theory to clarify the fundamental magnetic excitation structures, which are essential for discussing response properties to external fields. Finally, we present the hyperspace representation, which is employed to analyze the effect of phase degrees of freedom in spin moirés. We interpret a given spin moiré as the projection of a corresponding higher-dimensional one for systematic and efficient investigations of spin moiré engineering on spin textures and topological properties.