One thing you can do, if your pieces are big enough, is to sew them (right side in) to a used dryer sheet. Then just make a slit in the dryer sheet and turn them inside out, pillowcase style. I find this easier than trying to turn edges under as I go, and it will prevent raveling. Then you can either baste them to your fabric or use a temporary adhesive to hold them in place while you sew them down. When you cut your pieces, you'll have to add a scant quarter inch around each piece to allow for turning them inside out.