Jshep -
For me, it depends on the shape/size of the piece. If there's a nice 1/2" relatively straight section of applique, I leave that to last and use hemostats or a crochet hook to grab the paper and bring it out, then stitch up the last 1/2". The alternative is to make a 1/2" slit in the 'backing' fabric in the center of the appliqued piece and again use hemostats or crochet hook to grab and pull out the freezer paper through the back (often in torn pieces).