I use 3/8" wide ribbon, I prefer grosgrain. I use hot glue, so I put just a dab at the bottom of the headband, and start the ribbon SLIGHTLY below the bottom of the headband, and at an angle, not quite 45 degrees, and glue the ribbon to itself, if that makes sense. I wrap it around just like you would winding hair on a curling iron for "corkscrew" curls. Sides are touching each other, but not over lapped. I add just a tiny bit of hot glue every inch or so on the underside of the headband. When I get to the other end, I wrap just slightly past the end of the plastic to be sure it's not showing, cut & seal the end, and again with a tiny dab of glue, stick the ribbon to itself.
Hope that makes sense....late night writing is not always my clearest!