The next step is to make a frog with a button end. Nicky suggests a "single knot," but my single knot did not look anything like the photo, went through the frog loop too easily, and was not attractive. In the end, I chose a ball knot from these instructions, but I seriously considered using a square knot.
The square knot almost worked, and I think it would have been a good choice with thicker cord or a smaller loop. I use the "frog on a log" method of tying a square knot. I will show it here in case you don't know it.
Frog on a log . . .
Frog on a log (again) . . .
. . . and the log rolls over.
Now fold the end back around and under the frog counter-clockwise to re-make the first loop. Pin through the middle of the frog. It should look like this. (Pay no attention to the odd bits of cord at the right of the photo.)
Bring the end down and around clockwise to make the loop with the button on it. Adjust the placement of the button by tightening and loosening the knot until it's right where you want it. Unravel any extra cord from the live stitches at the end (beginning). Thread the unraveled yarn through the live stitches. Secure the loop by sewing both ends together behind the frog.
I used the cast-on tail to secure each corner of the frog to the garment. Since this garment had a folded hem, I simply tied the tails (from cast-on and bind-off) in a square knot on the wrong side, and hid each end of the knot in the hem. (If you don't know how to do this, let me know, and I'll show you!)