Remove all the mortar from around the loose brick, using a cold chisel and hammer, until it is free and can be removed. Lift the loosened brick out and set it in a bucket of water to soak. If the loose brick cannot be easily removed, or if the brick is broken, chop out the damaged brick with a wide brick chisel and hammer. Set the replacement brick in a bucket of water to soak.
Brush off any remaining loose bits of mortar from the hole with a stiff wire brush. Flush the cavity thoroughly with water.
Mix a small batch of mortar according to the manufacturer's directions. Dampen the bricks around the hole where the new mortar will be applied. Spread a thick layer of mortar on the bottom surface of the hole, and smooth it roughly level using a trowel.
Remove the brick from the bucket of water and shake it thoroughly to remove any excess water. Generously apply mortar to the top and sides of the brick using a trowel. Set the brick carefully into place in the prepared hole and align it with the bricks on each side of it. Apply additional mortar as needed.
Force mortar into the top and side joints of the brick to fill them in completely. Smooth the mortar with the trowel ensuring there are no gaps. Scrape excess mortar from the wall with the side of the trowel and shape the new mortar joints to match the joints in the rest of the wall.
Spray the mortar lightly with water several times a day for two or three days. When the mortar has set completely, use a stiff wire brush to remove any excess mortar from the face of the wall.