Another quick method, suitable particularly for large, simple shapes...
Trace your figure on a piece of fusible interfacing. Place the fusible side (shiny) on the right side of the fabric and hold it in place with pins (don't cut the figure yet).
Sew the fusible interfacing onto the fabric along the line you traced. Cut out the figure, leaving a seam allowance (1/4" or less). Clip the curves, making sure you don’t cut through the seam line.
Cut a hole in the middle of the fusible interfacing.
Turn the piece inside out, gently pushing the curves out with the tip of a pencil or scissors to give it shape.
Center the figure on your background fabric. Hold it in place by ironing it onto the background fabric. The fusible interfacing will bond with the background fabric.
The good thing about this method is that you don’t have to hold it in place with pins. For projects that will bear little use (like Christmas projects, brought out for a short time once a year), you don’t even need to sew the piece down. If your project will be washed repeatedly, however, it would be best to stitch it down (with an invisible stitch).