There are several different ways to quilt the center then attach the borders. One way is leave the backing whole, just roll up the border portion to keep it out of the way. Sandwich the center with the batting cut about 2 inches larger than the center. Quilt the center. Now lay the borders on the center quilted portion, right sides together and sew a quarter inch seam thru the whole sandwich. whip stitch a piece of batting for the borders to the center batting, then flip the border over & quilt that.
Another way is quilt the center and borders independently, then join using a QAYG technique, like this one:
http://www.quiltingboard.com/tutoria...l-t283918.html
There are others, basically all are variations of QAYG techniques. If you are planning on doing this for future quilts, a good reference is Marti Michell's 'machine quilting in sections'.
https://www.amazon.com/Marti-Michell...=marti+michell