I start with my machine set for a straight stitch. I then lower my needle and raise it up again. Then I pull the bobbin thread to the top and push the top and bottom threads out of my way (I'll deal with them later). Then I set my machine for the blanket stitch (or zig zag stich, or whichever I'm using for that particular applique) and go around the applique. When I get to the end, I take one extra stitch and again pull the bobbin thread up to meat the top thread.
Then I take the beginning thread (top and bottom that I pulled up earlier), thread it on to a cheater needle and bury the threads by inserting the needle one thread away from where the bobbin thread came up and run it under the top fabric and buried into the batting for about one inch or so (make sure your thread isn't showing on the backing fabric. Pull the threads through and snip close to the top fabric. Do the same for your ending threads.
Hope this makes sense. It's a lot easier to do than to explain!
