Determine the width and depth of the breakfast bar. The bar top should be at least 18 to 24 inches deep to accommodate serving trays, plates and beverages.
Measure two sections of 1/2-inch-thick plywood or hardwood to the width and depth of the bar with a measuring tape. Snap a chalk line along the measurements to create cut lines. Cut the sections along the chalk lines with a table saw.
Locate the studs behind the wall with a stud finder. Mark the stud positions on the wall with a pencil.
Cut a section of 2-by-4-inch lumber to the width of the breakfast bar with a circular saw. Place the lumber section on the wall 1 inch below the top of the finished bar. Place a carpenter's level on top of the lumber section and adjust the lumber until it is level.
Attach the 2-by-4-inch lumber section to the wall with 4-inch wood screws at each stud, using a drill equipped with a screwdriver bit. This section forms the back support for the breakfast bar.
Cut two sections of 2-by-4-inch lumber to a length of 17 inches. Miter the ends of the lumber sections at 45-degree angles with a miter saw.
Locate the wall stud closest to each end of the breakfast bar. Make a mark 8 inches below the bottom of the back support on the wall in front of the studs. Attach one of the mitered lumber sections at each mark with 4-inch wood screws so that the lumber section extends up and out from the wall at a 45-degree angle. These sections form the braces for the bar top.
Set one of the plywood or hardwood sections on top of the back support and braces. Secure the plywood or hardwood to the back support with 4-inch wood screws at 4-inch intervals. Insert 2-inch wood screws through the plywood or hardwood into the braces.
Apply wood glue to the bar top. Place the second section of plywood or hardwood on top and align the edges. Tighten C-clamps along the perimeter of the bar top and allow the glue to dry overnight.
Remove the C-clamps. Sand all surfaces of the breakfast bar with a palm sander to round the corners and smooth the surface. Apply wood stain or paint as desired to finish the breakfast bar.