This letter is the first part of a three-part tutorial focusing on rate-splitting multiple access (RSMA) for 6G. As Part I of the tutorial, the letter presents the basics of RSMA and its applications in light of 6G. To begin with, we first delineate the design principle and basic transmission frameworks of downlink and uplink RSMA. We then illustrate the applications of RSMA for addressing the challenges of various potential enabling technologies and use cases, consequently making it a promising next generation multiple access (NGMA) scheme for future networks such as 6G and beyond. We briefly discuss the challenges of RSMA and conclude the letter. In continuation of Part I, we will focus on the interplay of RSMA with integrated sensing and communication, and reconfigurable intelligent surfaces, respectively in Part II and Part III of this tutorial.