Cut backerboard sections to fit the interior of the fireplace that you want to cover. Set each piece inside, as it is cut, until you have all of the necessary pieces and have test-fit them all.
Use a hammer drill on the hammer setting to drill holes every 6 inches around the edges of each piece of backerboard, about an inch from the edge. Drill holes in a 12-inch grid on the inside of each piece of backerboard. Drill these holes just through the backerboard and slightly into the fireplace surface to leave a mark. Remove the backerboard pieces and set them aside.
Drill 1 inch into each marked screw hole with the hammer drill on the hammer setting at the highest power. Use a masonry drill bit. Back the drill bit out a few times on each hole to allow the masonry dust to escape. Replace the masonry drill bit if it gets worn out and stops drilling into the fireplace wall.
Apply a 1/4-inch layer of thinset on every surface of the fireplace where backerboard will be installed. Set the backerboard in place and attach it with 1-inch masonry backerboard screws. Drill each screw into the backerboard until its head is flush with the surface of the backerboard.