With years of hands-on carpentry experience, I recommend starting by measuring and marking the wall precisely where the table will go. Mark at the desired final height minus the tabletop thickness—for instance, if you want the top at 42 inches from the floor and the wood is 1-1/2 inches thick, mark at 40-1/2 inches. Note the center of the cleat and the centerline where the table will hang.
First, locate the wall studs using a reliable finder. Drill holes in the cleat to align with the stud centers for maximum strength. Secure the cleat firmly to the wall by screwing through these holes into the studs.
Position the decorative brackets on the wall, ensuring they are perfectly plumb with a level. Mark the wall through the bracket holes. Insert self-tapping drywall anchors at these marks, then attach the brackets securely by screwing through them into the anchors.
Lower the tabletop onto the cleat and supports, centering it carefully. From underneath, drive screws through the cleat into the tabletop to lock it in place for a rock-solid hold.