Robotic origami allows rapid prototyping of intelligent robots and machines constructed from thin sheets of functional materials. Multimaterial-based design freedom of origami robots creates functional versatility; however, the design parameters pose challenges in their mechanical layout and fabrication. While the conventional robot design follows a coherent and well-established design process, the construction of origami robots requires close study of their three-dimensional (3-D) and two-dimensional (2-D) geometries, compliant mechanisms, functional material specific components, and 2-D fabrication methods. In this paper, we report a systematic design methodology for building origami-inspired machines and robots based on these four essential design features. We provide their comprehensive formulation, comparing them to conventional robots and highlighting design challenges as well as potentials. We demonstrate the applicability of our procedure to the majority of origami robots in the literature and also validate it by designing a centimeter-scale jumping and crawling origami robot, Tribot, as a showcase. The 6-g Tribot crawls with fixed steps in a closed loop, adjusts its vertical jumping height by power modulation, and overcomes obstacles of 45-mm height by side jumps. This paper advances the design and fabrication methodology of origami robots, with customizable functionality from the ground-up.