My Olympic ring arrived yesterday, and because I’m curious (and clearly don’t value my time) I Googled the correct way to wear it. What I found was pretty interesting. From The Complete Book of Etiquette by Amy Vanderbilt, first published in 1952:
For as long as the wearer is in school, the insignia should face the wearer to remind him/her of the goal of graduation. Upon graduation, the class ring gains the status of a “badge of honor” similar to a diploma, with the effect that graduation entitles the wearer to display the insignia facing outward so that it faces other viewers.1
In sport, current athletes should wear the ring with the insignia facing them to remind them of their goals, whereas retired athletes should wear the ring with the insignia facing outward as a “badge of honor” and a representation of the terrific USOPA motto: Once an Olympian, Always an Olympian; Never Former, Never Past.