I have been looking into making my own synthetic quilt but have not found any information on how the edges of the insulation are sewn into the fabric. How are both sides of the quilt joined with the fabric to make a clean sewn edge?

just put the shell & liner right sides together with the insulation on top (not between fabric) sew 3 edges, then turn it inside out and sew the other.

Tim's got it, but you might want to trim the excess insulation from the outside edge of the seam before you turn the three pieces (2 shells and insulation) right-side-out. Also, hem the top edges of what will become the top of the quilt (thr head end) and form the drawstring casing as your first step - not the last. Also, you might want to sew around the 3 edges that form the sides and bottom, and part of the way around the fourth edge (the top with the casing), leaving an opening maybe 2 feet wide. That way, after you turn the quilt, it will be ready for the final stitches to close the opening through which it was turned right-side-out.