One of the most popular methods of applique is fused applique. quilters use a double sided adhesive ... usually something that irons on.
the shape is cut out of the adhesive material before it's laid onto the fabric.
then the shape is fused to the fabric.
**** completely forgot to mention that you next cut out the actual shape ****
then the fabric piece is fused to the background.
use a lightweight adhesive product so it'll be easy to stitch through by hand or machine.