I attached the new part by laying it under the original quilt and stitching the top and batting (of the new part) in the ditch of the original binding. Then folded a hem in the backing and finished that by hand. Since it has been several years ago that I did this I can't remember just exacty what I did. If you have any other questions feel free to PM me.
To answer Balloonatic's question...I saw no reason to take the original binding off...this just seemed the easiest way to add the new part. Besides that it gives it a nice look as well as giving me something to grab on to when I make the bed! (Actually, since retiring my DH makes the bed!!!)