When I use freezer paper for applique, I cut the freezer paper the shape it is supposed to be, then iron it onto the back of my fabric (just takes a second or two, no more to press it on). Cut the fabric about 1/4" away from the freezer paper. Then I take some spray starch and spray it into a small container to get it into a liquid state (the measuring thing from cold medicine or a camera film container is a great size). Dip a Q-Tip into the liquid starch and saturate the seam allowance of the fabric, then press it over the edge of the freezer paper with the iron. When you're done, you can remove the freezer paper and attach your applique to its backing. The starch will wash out and there's nothing left to make it stiff.
Clear as mud? :D
P.S. They now make freezer paper sheets that go in your printer, so you can print your designs on them. Pretty cool!