Start at the bottom picture...
When the first side is done, then go the the opposite side next. Repeat the same process. 
The back whip stitch. Start coming up through the edge of the binding. Go down just on the edge, almost under, the binding in the same spot you came up.
It's OK and preferred to catch some of the batting when you go under the quilt top/back fabric. Just don't go through to the other side of the quilt. You should not see these stitches on the under side.
When you come back up through the binding again remember to keep close to the edge as you catch the binding fabric.
When it's all pinned in place use a needle and hand quilting thread to back whip stitch this binding down. As in all the other applique you used you will want a thread the color of the binding, not the quilt fabric you are sewing it down to. 
Fold the finished edge over and pin it in place.
Once your first edge is sewn in place, this is what it will look like from the other side.
