For each button, you can drill 1 hole or 2 holes close together, depending on which method of tufting you wish to use. For two holes, try to match the holes in the buttons you plan to use.
Choose a fabric that will stand up to wear, especially if the headboard will see a lot of use as a backrest. Batting is sold in bags, and you will need 4 bags for 3 or 4 layers.
It will take at least 3 layers of batting to create a soft headboard. Adding more layers than that creates extra softness and a more pronounced look.
To tuft a headboard with two holes drilled for each button, simply loop the needle back through another hole in the button. Then push it back through the second hole in the plywood and pull it tight. Loop the needle back through the two holes a couple of times more, and then tie off the thread securely. With only one drilled hole, use a finishing nail to hold the thread in place. Loop the thread through the button and back through the original hole in the plywood. To keep the thread from simply pulling through the single hole, lay the finishing nail across the back of the hole and loop the thread over the nail and back through the hole. Repeat a few times and then tie off the thread to the finishing nail. Twist the nail to tighten the button down into the fabric to the desired depth. Use a staple gun and staple diagonally across the nail to secure it and keep it from unwinding