This monograph, written in a tutorial style, focuses on electromagnetic transient (EMT) simulation. These are becoming increasingly common, with significant active research, due to the introduction of inverter-based resources on the grid. A step-by-step tutorial is provided on performing an electromagnetic transient simulation for simple networks from the first principles, and concepts covered range from circuit simulation and Newton-Raphson to numerical integration with difference methods. This monograph should help graduate and senior undergraduate students, and working professionals, learn the inner workings of tools that perform EMT simulations. The tutorial uses a circuit-theory based approach to EMT simulation, and is introductory in that it shows the workings through several examples, expecting the reader to thereafter build further expertise through more detailed research. Nonetheless, the monograph should provide an excellent first step for anyone interested in the subject of electromagnetic transient simulation, especially those interested in building their own tools.