This article provides a tutorial on over-the-air electromagnetic signal processing (ESP) for next-generation wireless networks, addressing the limitations of digital processing to enhance the efficiency and sustainability of future 6th Generation (6G) systems. It explores the integration of electromagnetism and signal processing (SP) under a unified framework by highlighting how their convergence can drive innovations for 6G technologies. Key topics include electromagnetic (EM) wave-based processing, the application of metamaterials and advanced antennas to optimize EM field manipulation with a reduced number of radiofrequency chains, and their applications in holographic multiple-input multiple-output systems. By showcasing enabling technologies and use cases, the article illustrates how wave-based processing can minimize energy consumption, complexity, and latency, offering an effective framework for more sustainable and efficient wireless systems. This article aims to assist researchers and professionals in integrating advanced EM technologies with conventional SP methods.