I learned how to do that from Marti Michell's QAYG class. She has you sew the batting to the backing piece, 1/2" away from the edge. Just a straight line of stitching close to the edge of the batting which will only show on the back. If you don't want that line of stitching to show, you can attach the batting 1/2" from the edge with a fusible batting tape instead. Then you sew the top and back (with batting) to the side edges, flip them and do the top and bottom edges. I quilt on them as soon as I flip them. It works great.
If your quilt is already bound, you will need to cut it off before you add the borders.