With the rapidly increasing number of bandwidth-intensive terminals capable of intelligent computing and communication, such as smart devices equipped with shallow neural network models, the complexity of multiple access for these intelligent terminals is increasing due to the dynamic network environment and ubiquitous connectivity in 6G systems. Traditional multiple access (MA) design and optimization methods are gradually losing ground to artificial intelligence (AI) techniques that have proven their superiority in handling complexity. AI-empowered MA and its optimization strategies aimed at achieving high Quality-of-Service (QoS) are attracting more attention, especially in the area of latency-sensitive applications in 6G systems. In this work, we aim to: 1) present the development and comparative evaluation of AI-enabled MA; 2) provide a timely survey focusing on spectrum sensing, protocol design, and optimization for AI-empowered MA; and 3) explore the potential use cases of AI-empowered MA in the typical application scenarios within 6G systems. Specifically, we first present a unified framework of AI-empowered MA for 6G systems by incorporating various promising machine learning techniques in spectrum sensing, resource allocation, MA protocol design, and optimization. We then introduce AI-empowered MA spectrum sensing related to spectrum sharing and spectrum interference management. Next, we discuss the AI-empowered MA protocol designs and implementation methods by reviewing and comparing the state-of-the-art, and we further explore the optimization algorithms related to dynamic resource management, parameter adjustment, and access scheme switching. Finally, we discuss the current challenges, point out open issues, and outline potential future research directions in this field.