Decide the desired height of the bulletin board on the drywall. You would not want the bulletin board to be too high or low on the drywall. Mark the desired location of the bulletin board with a marker.
Use a stud finder to mark the location of a few studs behind the drywall. These studs will help you secure the bulletin board onto the drywall properly. Find as many studs as you possibly can.
Hold a sheet of paper, having the same size as the bulletin board, against the drywall section where you will be hanging the bulletin board. Transfer the location of the studs onto the sheet of paper.
Remove the paper sheet and place it over the bulletin board. Use marks on the sheet of paper to transfer the location of the studs onto the board. This will help you keep track of where exactly you would have to drill holes through it.
Use an electric drill with appropriate attachment to drill a few holes through the bulletin board. Position the board against the drywall, lining up holes in it with stud marks on the drywall. Be careful not to drill all the way through the studs. Instead, the holes should be more or less as deep as the screws would go.
Hold the bulletin board steady and install small screws through it and into the studs. Use a flathead screwdriver to tighten the screws. Be careful not to tighten the screws too much or you might end up damaging either the bulletin board or the drywall section onto which you are hanging the board.