Now, here is how I did it:
I bought a plywood board, standard sized, in a Norwegian hardware store.
I figured out the shape I wished for the bedhead. Here you can be very creative or keep it simple.
I found some examples of different bedhead's shapes on Pinterest:
A good tip to cut the foam is using an electrical knife (the one you usually use for the Sunday roast).
Then, I covered the foam with Dacron using spray glue to secure it. I shot a few staples on the back for good measure.
When I was finished with the front of my bedhead it looked that this:
Along the bottom of the back, I lined the rest of my fabric wrong side up and I nailed a stripe of cardboard on the top of it. This way, you get a nice even line at the bottom of the board.
I bought a nail spacer as well to keep an even distance between the nails. The nails kept falling down because of the thickness from the several layers, so I ended up by marking the spots where to punch each nail. A long process. You could also buy stripes of decorative nails, however they look fake and I wouldn't use them on this kind of project, where decorative details are important.