Step 1: Cold Hard Cash
Start with the side that reads "ONE" facing towards you on a flat surface. Like all money origami, a crisp bill will work best.
Flip the bill over, and fold the "white" edges on the top and bottom inward. Crease those folds, and return the bill to its original side.
Step 2: A Half Then a Quarter
Fold the bill in half. (You can flip this over to do it, or not. It doesn't matter.). Then fold the bill in half again.
Step 3: Making a Diamond
Fold the end of the bill up from the bottom. That "1" will be the center of the ring, and ideally you're trying to center to be even on both sides. The "white" of the bill gets folded under the "1."
Press everything down and crease.
Step 4: Ring Around the Finger (optional)
Just to get the shape of the ring, you can bend the folded bill around your finger a few times. It's not necessary to do this, however.
When you're done. place the bill back on a flat surface.
Step 5: Creating the Circle
This is one of those steps which is much easier to show than to describe. As seen below, fold the bill upward to create a 45 degree angle. The distance between this angle and the "1" will be the circumference of the ring.
Continue moving that fold under the ring, and back to the other side.
Step 6: Completing the Ring
Bring both ends of the bill together to form...a ring. Take the long end, and fold under the "1", tucking the folded end of the "1" under the long end.
Continue bringing the long end underneath the ring, and back around to the top.
Tuck the remaining flap underneath the "1", and press down all creases.
Step 7: Bling Bling!
And viola! You have a dollar ring.
*NB: If the ring is too small, as it will be for most men's fingers, there's a simple way to fix this not discussed in the original author's directions. You can skip the part of Step 5, where one wraps the bill around itself. Instead, just make the 45 degree angle fold (the first picture), and proceed to step 6.