After painting it, I attached 4 6-inch pieces of 2"x 4" lumber to the wall behind the bed where I wanted to mount the headboard. I attached each piece vertically on the wall where the four corners of the headboard frame would go. To attach each piece, I drilled 2 holes into the wall, inserted drywall anchors, and screwed the 2x4s into the anchors. Then, I used heavy duty picture-hanging hardware to hang the headboard onto the 2x4s.
Tada! Much nicer than a blank wall behind the bed.