Unfold the shelf brackets and hold them against the end of the existing counter, just below the countertop. When unfolded, the top of the bracket should line up with the underside of the existing counter. Determine where you want to place the brackets and use a pencil to mark the holes in each bracket on the counter support.
Mount the brackets. Drill holes for screws in each location you have marked, using a bit approximately the same diameter as your screws or wall anchors. Mount the brackets on the counter support using screws for solid counter supports and anchors for hollow ones. The bracket should sit flat against the vertical face of the existing countertop, with no wobbling or shifting.
Fully extend the folding shelf brackets and place the cutting board on top of them. Mark the position of the holes in the brackets on the underside of the cutting board as you did on the counter support in step 1.
Mount the cutting board. Drill holes corresponding to the marks made on the cutting board in step 3. Place the cutting board back onto the brackets and screw it firmly into place.