Now for the "real" sewing.. I hope these pictures are clear enough for you to see. Applique is the only time in hand piecing a quilt that I use knots in my thread. with a short to moderate thread in your needle I make a knot in the end.. then I will work the needle into the quilt piece's folded under edge and push the needle out right through the fold.
then I find where the edge of that quilt piece should meet the background and take a small stitch in the background fabric.the I slip the needle into the "hem" of the quilt piece and take another small stitch right next to the first one. You continue around the edge of the piece first taking a small stitch in the "hem" of the quilt piece.. then a small stitch in the background fabric.
Each time I take a stitch I try to line up my stitches so that the needle "piercing" of the fabric are right above each other.. does that make sense? if not let me know I'll try to clarify. I try to keep my stitches around 1/8" or so long.. and use only gentle tugging to keep things together.. you don't want to pull it too tight as that will pucker things up. When you have gone all around the piece or come to the end of the seam I bring the needle to the back of the backgound and taking a small stitch on the back in the seam allowance, I tie off that thread and prepare to start again.