We introduce and discuss the Schwarzschild metric, at a level suitable for beginners with basic calculus knowledge. First, the exterior vacuum metric is examined, and several techniques about how to work with metrics are demonstrated, and their physical significance explained. A geometric understanding of the various terms in the metric is developed, and some fully worked examples are given. We then progress on to the interior metric, and present its peculiarities and physical consequences. This leads on to a discussion of Schwarzschild black holes, the meaning of event horizons, and what physically happens if we allow a test particle to freely fall into such black holes, from the points of view of different observers. Animations and a video are presented that help visualise these principles.