Multiple access is the cornerstone technology for each generation of wireless cellular networks and resource allocation design plays a crucial role in multiple access. In this paper, we present a comprehensive tutorial overview for junior researchers in this field, aiming to offer a foundational guide for resource allocation design in the context of next-generation multiple access (NGMA). Initially, we identify three types of channels in future wireless cellular networks over which NGMA will be implemented, namely: natural channels, reconfigurable channels, and functional channels. Natural channels are traditional uplink and downlink communication channels; reconfigurable channels are defined as channels that can be proactively reshaped via emerging platforms or techniques, such as intelligent reflecting surface (IRS), unmanned aerial vehicle (UAV), and movable/fluid antenna (M/FA); and functional channels support not only communication but also other functionalities simultaneously, with typical examples including integrated sensing and communication (ISAC) and joint computing and communication (JCAC) channels. Then, we introduce NGMA models applicable to these three types of channels that cover most of the practical communication scenarios of future wireless communications. Subsequently, we articulate the key optimization technical challenges inherent in the resource allocation design for NGMA, categorizing them into rate-oriented, power-oriented, and reliability-oriented resource allocation designs. The corresponding optimization approaches for solving the formulated resource allocation design problems are then presented. Finally, simulation results are presented and discussed to elucidate the practical implications and insights derived from resource allocation designs in NGMA.