Put on a pair of work gloves, safety goggles and a facemask to avoid injury from flying brick shards, or inhalation of mortar particles.
Remove as much of the spalled material as possible from the brick using the tip of a cold chisel.
Drill holes into the mortar around the spalled brick about 1/4-inch apart and as close to the base of the brick as possible. Cut smoothly through the mortar without affecting the adjacent bricks with a masonry bit in your drill.
Place the point of a cold chisel onto the mortar, overlapping two of the drilled holes. Hit the head of the chisel with a rubber mallet to cut through the intact piece of mortar. Cut through all of the mortar around the bricks using the same method, working around the top, down both sides then undercutting the brick from the bottom.
Clear out the broke mortar from the joints around the brick with the chisel. Pull the spalled brick from the opening.
Chip away any large mortar pieces remaining in the cleared space with the chisel. Brush out the opening with a wire brush.
Mix a small batch of mortar in a bucket. Add the dry mortar mix to the bucket then stir in the water with a stick until the mortar is the same consistency as peanut butter.
Wet the bricks on all sides of the opening with water to prevent the bricks from leeching away new mortar.
Apply a layer of mortar with a steel trowel to the bottom of the empty space in the brick face to a level slightly higher than the surrounding mortar line. Press the replacement brick onto the mortar firmly, pressing the mortar beneath down until level with the surrounding mortar line.
Apply a tuckpointing trowel to fill in the joints surrounding the brick with new mortar. Pack the joints completely to the level of the brick. Go over the applied mortar with a rounded stick, removing any excess until the mortar is the same height as the surrounding lines
Wipe any excess mortar from the face of any bricks it spilled onto with a damp sponge. Allow the mortar to cure for 48 hours before touching the brick face.