OK, now that you've clarified...here is what you do. Sew together your quilt top however you'd like -including BORDERS. This is the step that I think you've already done...so
Next is the sandwiching step. Cut your backing to be approximately 4" or so wider AND longer than your top. Lay it pretty side DOWN on your surface. Lay your batting (also cut larger than your top) as the next layer.
Top with the top of your quilt. Baste, then quilt. Be sure to read threads on this board about sandwiching and basting for some excellent tips
Now...you square up your top(trim the excess making sure the sides/top/bottom) are all straight). Now is when you sew on your BINDING. I like the double fold, so I cut mine 2 1/2" or 2 1/4". Make 1 long strip...long enough to go all the way around the quilt plus a little extra. Fold the binding in half (longways) with wrong sides together and press. Place the raw edge to the edge of your squared off quilt on the FRONT side and sew on using your walking foot. There are lots of good tutorials on this board about how to put on binding and how to do the mitered corners Flip it over to the back side and attach with your chosen method.
Good Luck!!