Fold the rectangle in half lengthwise and pin along the edge matching up the seams. Measure down 1 1/2" from the top and put a pin in then measure down another inch and put another pin in. Sew all the way down the side leaving the space between the pins unstitched (this is for the drawstring) make sure to anchor your stitches either side of the space so they don't unravel later.
You should now have a tube that is starting to look like a bag holder. Finger press the side seam open at the top and fold the top edge down to just above the space. Stitch the hem of the casing all the way around the tube just under the space. Your drawstring casing is now done.
Sew a hem on the bottom edge of the tube to form the elastic casing, leaving a little gap to thread your elastic through ( about 8" of thin elastic). I tied mine in a knot instead of sewing it but that's up to you. Thread some nice looking trim (rope, ribbon, cord etc) into the drawstring casing and cut off a whatever length you want and knot the two ends together so it can be hung up on a hook. That's it, now you have a nice plastic bag holder to replace the old yucky one that you keep meaning to get rid of but never do!