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.