If using a sewing macine use the zig-zag stitch on a 2 setting for the thread and sew around the edges of the applique. If doing it by hand sew it on like you would a the edges of a button hole.
The sturdiest way to do it is with a zigzag stitch as close to the edges as you can get, this way it will definitely stay in place and also give the applique a nice, edgey look.
