Drill holes around the corners of the bricks you intend to replace by using a masonry bit in a hammer action drill. Drill additional holes along the sides of each of the bricks, making a line of holes. This will help loosen the mortar and create gaps around the edges of the brick.
Insert the narrow tip of a concrete chisel into the crumbling mortar joint. Use a hammer to chisel out the remaining mortar from around the sides of the brick. Wiggle the loose brick to detach it from wall. Use your chisel and hammer to remove any stubborn bits of mortar from inside the hole left by the removed brick.
Mix up the mortar, according to the package instructions. Press mortar on the bottom surface of the hole, using a small trowel. Spread mortar over the sides and top of the new brick. Press the brick into the gap, wiggling it into place and making it even with the surrounding bricks. Apply more mortar around the edges of the brick to fill the gaps. Use a pointing tool to push the mortar into any gaps or air pockets.
Use a clean trowel and rag to scrape and wipe the excess mortar off the front of the replaced brick and any nearby bricks. Run the tip of your raking tool around the edge of the replaced brick, making a groove that matches the grooves around the existing bricks in the remainder of your wall. Replace any other damaged bricks along the length of your exterior wall in this same manner.