I am an avid Pinterest-er, and as soon as I saw this project I knew it would be useful and something I would want, so when I got engaged it was one of the first DIY's on my list.
Turns out it's super easy, all you need is a small frame, the cardboard that came in the frame (glass not needed, you can find glass-less frames at thrift stores super cheap), felt, and a pushpin.
Note: I didn't use the white felt at all.
I cut out a piece of felt the size of the cardboard in the frame, figured out where I wanted the ring to hang and embroidered a little leaf pattern around it.
Stack your embroidered felt on the cardboard and stick your pin in the right place, bending it 1/4-1/2" away from the ball at about a 45 degree angle. Tape the pin to the backside of the cardboard, put it back in the frame, and voila!
You got yourself a ring frame.
I put mine above the sink so I don't have to wear my ring when I do dishes.