Measure the thickness and length of your shelf.
Cut three wood strips to a length equal to the length of your shelf, plus 2 inches. For example, a 30-inch shelf would need strips cut to 32 inches long. Take the width of your saw blade into account while cutting.
Cut two other wood strips to a length equal to the thickness of your shelf. A one-inch shelf would need one-inch strips. Take the width of your saw blade into account while cutting.
Arrange the two short strips and two of the three long strips into a rectangular frame. The 2-inch edges of the short strips should abut the 2-inch faces of the long strips. Glue in place, then reinforce with three 1 1/2-inch wood screws per connection, a total of 12 screws.
Cut the remaining strip to a width that matches the total width of the frame you've built. Mount that strip to the back of the frame using wood glue and six evenly spaced 1 1/2-inch wood screws per long strip.
Sand all faces of the bracket. If desired, paint or stain to match or complement the shelf.
Mount the bracket to the wall using 3-inch wood screws, each drilled through the back plate and into a wall stud behind. Position the bracket so it crosses at least two wall studs.
Coat the inside of your bracket with wood glue. Slide your shelf into the bracket, then screw in place with one 1 1/2-inch wood screw for every 2 inches of board length. Screw in place on both the top and bottom faces. Wipe away excess glue.