Hi phyllis,
You can definitely sew this on the machine. I would recommend doing it that way to be sure that it holds – plus it’s difficult to sew through 2 layers of elastic by hand, which I’m sure you discovered! 🙂
What you can do is pull the two ends of the elastic so that they are far from the skirt and the skirt is all bunched up on the elastic in the casing. This way you aren’t stuck trying to sew in such a small spot. Set the skirt to the side out of your way and just hold onto the elastic. Take your time and lay it flat where you want to sew it. I usually use a single pin to keep the overlap where I want it until I start to sew.
Once you have the elastic flat and lined up under the needle (with nothing pulling or twisting the elastic), begin sewing your square. When you get to a corner of the square, leave the needle down through the elastic and lift the presser foot, then rotate the elastic assembly, lower the presser foot and sew the next side of the square. Continue on this way until you’ve completed the square.
To lockstitch at the end, you will sew several stitches with a zero stitch length – in other words, the fabric (or elastic in this case) doesn’t move. You can also do a backstitch. This is where you sew a few stitches in reverse. Either way just keeps the stitching from coming undone.
One small, but helpful, tip: When you get to the 4th side of the square, instead of simply turning the corner, you can rotate your work back the other direction until you are lined up for that final side. You’d turn backwards 270 deg instead of forward 90 deg. This way you don’t have to turn the entire project through the small space between the needle and the machine.
I hope some of that made sense!