Autonomous Underwater Vehicles (AUVs) represent cutting-edge technology in marine robotics, engineered to navigate the intricate and challenging environments of the ocean depths autonomously. Central to their navigation prowess is the control of yaw motion, governing the horizontal orientation and direction of movement. In this study, a comprehensive analysis of AUV yaw motion control is undertaken, encompassing the development of governing equations, numerical simulations, and controller implementation. Through numerical simulations, the relationship between the resisting moment encountered during yaw motion and the resulting motion dynamics is explored in depth. Moreover, both Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers are tested and compared regarding their effectiveness in controlling AUV yaw motion. The findings reveal that the PID controller exhibits superior performance, characterized by reduced oscillations and errors, thereby enhancing the precision and stability of AUV navigation in dynamic underwater environments.