Pat, a birthed (or envelope, or pillowcase) style quiltis one where you make a sandwich of batting, backing then top, with the last 2 right sides together. You sew most of the way around the outside, turn it right side out, then sew up the part of the edge you left open.
Notes: It is important to have a fairly stable batting (I use thermore, which is VERY stable). The batting and backing should also be well pressed with starch or sizing, which also stabilizes the whole thing. After I turn it right side out , and have sewn the opening, DH and I 'play tug of war'. We pull the whole thing on each diagonal and pull it firmly lengthwise. This seems to help get the 3 layers to grab each other. I then pin baste quilte well before quilting. If I am going to do complex FMQ, I first do a basting stitch along the center in each direction for additional stability. Otherwise, I quilt centerlines and work out from there. I have wrists that give me trouble if I tie, so I never do.