Simulating NMR experiments may appear mysterious and even daunting for those who are new to the field. Yet, broken down into pieces, the process may turn out to be easier than expected. Quite the opposite, it is in fact a powerful and playful means to get insights into the spin dynamics of NMR experiments. In this tutorial paper, we show step by step how some NMR experiments can be simulated, assuming as little prior knowledge from the reader as possible. We focus on the case of NMR at zero and ultralow fields, an emerging modality of NMR in which the spin dynamics are dominated by spin-spin interactions rather than spin-field interactions, as is usually the case with conventional high-field NMR. We first show how to simulate spectra numerically. In a second step, we detail an approach to construct an eigenbasis for systems of spin- 1 / 2 nuclei at zero field. We then use it to interpret the numerical simulations.