This is what I started with.
I used a seam ripper to undo the hem. If you think the amount you cut off the skirt is wide enough, you can just cut off the hem. Keep in mind you'll be folding it in half, so it will be half as wide.
Cut the circle along one of the side seams so that it is now a long strip of fabric. Fold the fabric in half lengthwise with right sides together and sew along the edge, leaving the ends open.
Now you'll have a long tube. Flip it so the right side is out and iron about 1/2 inch to the inside of the tube.
Twist the tube once in the middle. This makes it an "infinity" scarf.
Tuck the raw end of the tube into the ironed end. Pin together and sew.
Ta-da! That's it. You could easily do this with just a strip of fabric too, but it's good to use up scraps from other clothing!
Have a good weekend, everyone! :)