Starting with the appliqué piece of your choice, bring your needle from underneath to the top, coming up right through the line you drew when tracing the template. Fold under the seam allowance and bring your needle back down through the wall hanging fabric (only the top layer though!) and then straight back up through the edge of the appliqué piece, about 1/8” away from where you went down.
I highly recommend watching the video linked above for this step, as it is much easier to demonstrate than it is to explain in words.
Continue all the way around the appliqué piece, sewing on the line you drew.
Corners, curves, and points:
Any curves, corners or points that go in towards your appliqué piece will need to be snipped on the seam allowance to ensure that there is no tugging. Make a small snip to, but not through, the line you traced onto the fabric as you reach these parts.
To tie off your thread, take the needle through the top layer of your wall hanging and create a loop with the thread. Run the needle through the loop to form a knot.
Then insert the needle down into the wall hanging and back up about 1” away, tugging the knot you made into the wall hanging. Pull the thread taught and snip it right next to the wall hanging so when you release it the thread will retreat back into the wall hanging.