Thanks again everyone!

To make it, I used the steel block shown in the second set of pics as an anvil. You hold the coin and tap it on the edge with the ball pein part of the hammer. Then, rotate the coin a little and tap it again. Keep rotating the coin while constantly tapping it, and the metal will start to mushroom out as the diameter decreases.
Once it has reached close to the desired diameter for the ring size you are going for, you have to drill out the center. I found many different ways of doing it online so here is my method: I use a set of vise-grips with the round, crescent-shaped jaws and line the jaws with a thick piece of leather from an old belt. I tighten the vice grips just enough to secure the coin, but not too much pressure to bend it (especially important once a hole is in the middle, not as structurally stable).
I then use a normal drill bit to drill a large enough hole to fit a dremel sanding drum inside it. You have to be very careful here so that the drill bit doesn't catch and spin the coin loose as it could damage it. Once you can get a dremel sanding drum in, it is pretty easy from that point.
I found the sanding drums work better than the metal grinding bits they have. The metal grinders, when spinning fast enough to not stall out, get so hot that the silver basically melts into the crevasses, clogging them up. The sanding drums don't do this as bad.
Once it is sized right using the dremel, I finished by lightly polishing it using 0000 steel wool. I didn't want to remove the hammer marks, so I didn't use polishing compound like they do in the link above.
Thats all there is to it. Really a kind of fun, simple project.