A piece of wood preferably with an interesting grain pattern (I used wenge)
Some sort of finish
Step 2: Drill the outer hole partially
Guesstimate what the outer diameter of the ring should be, depending on the size of your finger and choose a hole saw accordingly. Using a drill press, drill part of the way through your piece of wood, making sure that the piece of wood being drilled stays intact with the board.
Step 3: Drill the inner hole fully
Put a forstner bit a little smaller than your finger into the drill press and drill a hole through the center of the outline you've already drilled.
Step 4: Finish drilling the outer hole
Put the hole-saw back in and finish drilling the outer hole. Pull the ring-shaped piece of wood out of the hole-saw.
Step 5: Sanding galore
Use a small drum sander attachment to sand the inside of the ring to the appropriate width. I used a larger drum sander attachment to sand away the machine marks on the outside, but you can use whatever method you want.
Step 6: Getting it down to the right size
I was afraid of cutting myself, so instead of cutting the ring down to the correct with, I just sanded it a bunch with a belt sander.
Step 7: Final sanding and finishing
I suggest hand sanding after you've got it down to the size you want. You also might want to round out the edges. I used paste wax to finish it. Some type of oil would probably also work well. I'd be careful using anything like lacquer or polyurethane because the coat might go on too thick and then it wouldn't fit your finger. Now, you should either have a beautiful ring or a useless, mangled piece of crap. If you should have a useless, mangled piece of crap, repeat steps 1-6.