You might try not putting the border on until you've finished quilting the main part if both the back and front are the same size. Leave some extra batting sticking out all around the quilt.
Working one side of the quilt at a time, just line up the border fabric, front and back (right sides together) so that they your sandwich would be all the raw edges lined up: front border, quilt front, batting, quilt back, and back border. Stitch throught all five layers, then fold the borders back over the batting. Do this for each side of the quilt.
You'll want to decide how you want to do the corners first. You will have to fuss as you could miter the corner or not. Which order you attach will the border will affect how the corners come out. After the borders are done, trim and add your binding.
Hopefully, this isn't too confusing.