Attaching anything to block or brick surfaces used to be a hassle. If you were lucky, if the block didn't break, or if the fastener wasn't overtightened, it would hold, for a while. But not anymore. Tapcon style concrete anchors are nearly as simple as wood or drywall screws.
Cut 2x4 inch treated lumber for ledger boards the same length as the width of your panels. We will assume a panel 2 feet wide by 4 feet high. You will need three pieces, each 24 inches in length.
Set the ledger boards on a level, sturdy work surface. Use a drill with a 1/4 inch wood bit to drill three pilot holes in each ledger board. One should be centre, and one each centred top to bottom 2 inches from either end.
Determine where the panel will be installed. Mark the four corners of the panel on the wall at the proper height and placement. Place one of your ledger boards between the top corners and just under the top of the panel placement.
Use a 3/16 inch mason's bit to drill through the pilot holes in the ledger board 1/8 inch into the block surface. This will serve to mark the location of the pilot hole in the wall.
Repeat the process with the second ledger between the two bottom corners a little above the bottom of the panel placement, and the third spaced halfway between the first two.
Drill all of the pilot holes to a depth of 1 3/4 inches with the 3/16 inch mason's bit. Blow the dust from the holes before proceeding.
Place a ledger board against the wall with the pilot holes lined up. Drive a 3 inch Tapcon style concrete screw into each hole. Use the recommended screw tip to avoid stripping the screw heads. Repeat the process with the other two ledgers.
Place the wood panel on a level surface. Carefully drill two pilot holes through the panel in line with each ledger board. Use a 1/8 inch wood bit.
Hold the panel in place and drive a finish head wood screw through the panel into the ledger board. Repeat for each of the six pilot holes. Use screws an inch longer than the thickness of your panel. We will assume a thickness of 3/4 inch, so you would use a screw 1 3/4 inches long.
Fill the screw holes with wood filler for stained wood, or painter's caulk for painted finishes. Retouch the finish with the appropriate stain or paint.