An approx 12" section of the empty roll from either paper towel, or wrapping paper, I use the most sturdy roll I can find. Then I thread a 1" piece of fabric, long enough to go through it and then tie it together and wrap it around your neck (you have to play with this to find the most comfortable length). Then, once I have pressed my binding in half, I carefully wrap in around this tube and then put it around my neck and it feeds from the tube as you sew the binding onto your quilt, keeping it from getting wrinkled or twisted or falling to the floor.
As with everything else quilting related, it takes a bit of practice but once you get the hang of it. It is very easy. Sometimes, I make my bindings ahead of time (on a good day) and they stay on the tube, hung on a hanger, until I am ready to use them, without getting beat up.