Unmanned Aerial Vehicles (UAVs) represent a rapidly increasing technology with profound implications for various domains, including surveillance, security, and commercial applications. Among the number of detection and classification methodologies, radar technology stands as a cornerstone due to its versatility and reliability. This paper presents a comprehensive primer written specifically for researchers starting on investigations into UAV detection and classification, with a distinct emphasis on the integration of full-wave electromagnetic computer-aided design (EM CAD) tools. Commencing with an elucidation of radar's pivotal role within the UAV detection paradigm, this primer systematically navigates through fundamental Frequency-Modulated Continuous-Wave (FMCW) radar principles, elucidating their intricate interplay with UAV characteristics and signatures. Methodologies pertaining to signal processing, detection, and tracking are examined, with particular emphasis placed on the pivotal role of full-wave EM CAD tools in system design and optimization. Through an exposition of relevant case studies and applications, this paper underscores successful implementations of radar-based UAV detection and classification systems while elucidating encountered challenges and insights obtained. Anticipating future trajectories, the paper contemplates emerging trends and potential research directions, accentuating the indispensable nature of full-wave EM CAD tools in propelling radar techniques forward. In essence, this primer serves as an indispensable roadmap, empowering researchers to navigate the complex terrain of radar-based UAV detection and classification, thereby fostering advancements in aerial surveillance and security systems.