What a kind gesture. I'm sure your neighbor will love it!
When you say, "pillowcase quilt," do you mean sewing it together with right sides together and turning it right side out? If so, I put my batting on the bottom, backing on top of the batting with right side up, then put the quilt top on top with the right side down. Pin it all together and sew all the way around, leaving about 12" to turn. Close the opening by hand, then top-stitch all the way around about 1/2" away from the edge. It works pretty good. Then you can tie or quilt as needed.