As a prominent member of the next generation multiple access (NGMA) family, non-orthogonal multiple access (NOMA) has been recognized as a promising multiple access candidate for the sixth-generation (6G) networks. This article focuses on applying NOMA in 6G networks, with an emphasis on proposing the so-called One Basic Principle plus Four New concept. Starting with the basic NOMA principle, the importance of successive interference cancellation (SIC) becomes evident. In particular, the advantages and drawbacks of both the channel state information based SIC and quality-of-service based SIC are discussed. Then, the application of NOMA to meet the new 6G performance requirements, especially for massive connectivity, is explored. Furthermore, the integration of NOMA with new physical layer techniques is considered, followed by introducing new application scenarios for NOMA towards 6G. Finally, the application of machine learning in NOMA networks is investigated, ushering in the machine learning empowered NGMA era.