Measure the height of the fireplace and cut the furring strips with the saw. The furring strips are 1 by 2 inch or 1 by 3 inch strips of wood used to fasten drywall to them.
Attach the furring strips to the brick fireplace vertically starting from the edge of the fireplace. Attach a strip on every corner and 16 inches apart from each other. Hold the furring strip in place and drill a pilot hole. Fasten the strip in place with the masonry screws. Attach a screw every 12 inches on the furring strip.
Measure and, with the utility knife, cut the drywall to the size needed to fit the fireplace.
Hold the drywall in place and secure it with drywall screws. Attach the screws to the furring strip 2 inches from each edge and then every 6 inches.
Secure the corner beads to the outside corner of the drywall with drywall screws every 6 inches. Attach the drywall tape to all seams between the drywall pieces and inside the corner angles.
Apply compound over the corner bead, the drywall tape and the drywall screws. Use the spatula to apply a thin layer of compound. It must overlap the targeted area by at least 6 inches. Let the compound dry overnight. Lightly sand the compound and apply a second layer. Let the second layer dry overnight and sand it smooth.
Finish the drywall to your liking. You could paint it or install tile over it.