We present a tutorial-introduction to the synthesis of Liveness Enforcing Supervisory Policies (LESPs) for Discrete-Event Dynamic Systems (DEDS) modeled by Petri-Nets (PNs). The tutorial is aimed at researchers unfamiliar with the area, and the objective is to develop a working knowledge of concepts and results from the area. We start by introducing PNs as a modeling tool for DEDS. We motivate the liveness problem through examples. Following this, we present relevant theoretical results on the computational aspects of LESP synthesis for PN models of DEDS, along with other results and methods. We conclude the paper by listing some new directions in the area.