I have only started dabbling in hand applique. Because you say your machine is dying, I am assuming you are asking about hand techniques. So far my favorite is the freezer paper method. I make a template of the shape with FP (reversed) and then iron it on the back of my fabric. Cut it out with 1/4" seam allowance and then do needle turn to turn my edge under as I sew using my freezer paper as a guide. This method requires that you cut a slit or cut away your back ground fabric to remove the freezer paper. If you are careful, you can reuse the FP template several times before it quits sticking.