I'm not a big fan of doing applique, but I love the patterns and the fact that really nice things can be made with applique. Therefore, I've started doing some. I would stitch around the pieces- I like the blanket stitch, but if you have a machine with decorative stitches, many of them can be used for applique. Start with the pieces that are in the background first or inside the larger pieces. Then when you stitch the larger pieces it helps to lock in the stitches on the others. Also if you are going to quilt it, the applique stitches can be your quilting. Then the background can be stitched so the applique design stands out. I hope this makes sense.