With the advancement of wireless communication to sub-terahertz (THz) and millimeter-wave (mmWave) bands, accurate channel models and simulation tools are becoming increasingly important for modeling a wide range of frequencies and scenarios. This paper provides a comprehensive tutorial on generating drop-based and spatial consistency-based channels using the open-source MATLAB-based NYU Channel Model Simulator (NYUSIM). NYUSIM is built on extensive real-world radio propagation measurements for the frequency range of 0.5-150 GHz, covering a variety of scenarios such as Urban Microcell (UMi), Urban Macrocell (UMa), Rural Macrocell (RMa), Indoor Hotspot (InH), and Indoor Factory (InF). Additionally, an overview of the evolution of simulators used to design and analyze wireless systems since the early days of cellular communication is also provided. We introduce the most popular types of simulators used in academia and industry, such as Channel Simulators (CSs), Link Level Simulators (LLSs), System Level Simulators (SLSs), and Network Simulators (NSs), to study wireless communication systems for 5G and beyond. Owing to the widespread adoption of the 3rd Generation Partnership Project (3GPP) Stochastic Channel Model (SCM) for channel generation in various simulators, we conduct a comparative analysis between the 3GPP SCM and NYUSIM channel model to highlight their differences. Moreover, NYUSIM's versatility extends beyond its MATLAB implementation, as it can be implemented in various LLSs, SLSs, and NSs, enabling researchers to incorporate realworld measurement-based channels into their simulations. To illustrate this capability, we showcase NYUSIM's implementation in ns-3, a widely used open-source discrete event network simulator. Additionally, we provide several applications of NYUSIM to highlight its potential uses.