In the video above, from Rio Grande, they’re not using a coin, but are showing the process of creating a washer shape and making it into a ring.
If you prefer non-video ways of learning, here are three tutorials for you:
A series of photos showing the process of taking a quarter and turning it into a ring:
Here’s one with a half dollar, it’s also a longer and more detailed post:
And one more, in this one, they take away the words on the quarter:
It occurs to me the same method could be used with metal clay, to make a seamless ring. Has anyone tried that?