Cut the board your desired length - usually a little narrower than the item you are hanging.
Make a 45 degree angle cut along the entire length of the board.
Screw one side to the wall as shown.
Then screw the other side to the item you are hanging.
Slide the headboard or shelf or mirror onto the clete alredy installed onto the wall.
Wallah !!!!! Be sure and read the BLOG post about hanging headboards and small tables using a French Clete.