Measure up 48 inches from the floor with your tape measure. Make a pencil mark on the wall.
Run the stud finder along the wall and mark the position of three studs in the vicinity of your pencil mark. The studs will be spaced 16 inches apart from each other. Measure up from the floor along each stud and make a mark 48 inches up from the floor.
Hold a shelf bracket against each stud so the top edge is even with the pencil mark. Screw the bracket into the wall and stud with wood screws and a screwdriver. Repeat with the other two brackets and stud locations.
Place your 3-foot board on top of the brackets, spaced evenly on both ends, relative to the outer brackets. Attach the board to each bracket with wood screws, from the bottom of the bracket.