I recommend this method for very small pieces and/or for that "folk art" feel.
Trace your template onto a piece of fusible interfacing. Do not cut it out yet.
Iron the fusible interfacing (shiny side down) onto the wrong side of your fabric. Make sure it is well adhered, especially around the edges.
Once it has cooled down, cut out the figure.
Center the figure and hold in place with pins on the background fabric. Use two to three strands of embroidery thread (the same color as the piece being applied, or in a contrasting color) and sew the figure to the background fabric, using a buttonhole of "blanket" stitch (see below).
Blanket stitch: Use the photo as a guide for this stitch. The needle comes from the back up point A (along the edge of the piece being applied). Move over to the left a little and push the needle through point B, coming up again through point C and over the thread. The most important think to keep in mind here is uniformity - try to keep your stitches even, both in length as well as with regard to the space between stitches.