The way the fusible thread works is that you use it in the bobbin, and you use monafilament in the needle. Then you sew just inside your drawn line on each applique piece. You cut them out as close to the line as you can, then fuse them with an iron onto your backing fabric. The iron melts the monafilament so you can pull it off, and you're left with your applique piece fused to the background. Then you can just satin stitch around.
It was pretty easy--I'm just not great at the satin stitching part!