I bought this silicone egg ring for making scrambled eggs for breakfast sandwiches. It's so cute!
My procedure:
Squirt ~ΒΌ cup of water in the pan (this will be used to steam the top side of the egg). Make sure you have the pan's lid ready to go.
Use some non-stick spray to coat the inside walls of the ring.
Put the ring in the pan, put a tiny pat of butter inside the ring, then pre-heat the pan until the butter is very melted or begins bubbling. The water should be boiling as well.
(The butter serves as a pre-heat indicator more than anything, since you want the bottom of the egg to set quickly. When preheating, you want to focus your attention on how hot the pan is inside the ring.)
Put one egg inside the ring (possibly scrambled, if wanted), and immediately put the lid on the pan. The steam should help cook the top side of the egg.
Optionally, if the egg doesn't seem to be done throughout, you can flip it over and finish cooking the top side.