The significant technological advances in the industry of low earth orbit (LEO) satellites have opened the door to a new realm of LEO-based applications. One key application is providing internet broadband services to people everywhere around the globe. The main driver to achieve such satellite-based global connectivity is deploying large numbers of LEO satellites at a set of altitudes, ranging from 300 km to 1500 km. Given that we have multiple competing companies launching various constellations with diverse altitudes and numbers of satellites, we can envision a set of spheres concentric with the earth with large numbers of LEO satellites distributed on the surfaces of each of these spheres. To enable accurate modeling and optimal design, we need to think of creative techniques to enable mathematically analysing such communication systems. In this tutorial, we discuss a recently proposed mathematical framework that enables tractable analysis of LEO satellite-enabled communication systems while capturing the influence of satellites’ numbers and altitudes as well as the spatial distribution of earth stations. Firstly, we describe how this stochastic geometry-based framework is modelled and discuss its accuracy. Next, we provide a detailed example where this framework can be used for coverage analysis. We then introduce and discuss integrated space-aerial-terrestrial networks. Finally, we discuss how this framework can be used to study routing and end-to-end latency analysis in such networks. Realistic values from existing constellations, such as OneWeb and Starlink, are further used as case studies in this tutorial.