Let me know if this doesn't make sense.
One way that I learned to do this was to trace my applique shapes onto the dull side of freezer paper. Cut out. Iron the shiny side onto the wrong side of the applique fabric. Cut around the shape leaving about 1/4 inch all the way around. Glue this edge with a regular washable glue stick to the paper side of the freezer paper. Pin into place and whip stitch with little stitches, as invisible as you can make them onto your background fabric (with matching fabric. I really like YLI silk thread if you can find it). Then you could always use a blanket stitch with floss if you wanted to for a decorative touch. Oh, then when your sewing is done, make a careful slit in the middle of your applique (background fabric) and clip away the background to about 1/4 inch of your applique (on the wrong side again). Pull your freezer paper shape out. You may have caught a few places with your stitching so be careful and ease it out.
Phew, that sounded like a lot of steps. I do seem to be attracted to complicated processes. But this method makes sure that you don't have a raw edge.
lots2do