Cut into the broken bricks with a diamond blade power cutter. Make several small cuts and move slowly to ensure you do not cut the surrounding bricks.
Chisel away at the bricks, using the cuts you just made with the diamond blade as a starting point. These cuts make the brick weaker and easier to chisel away.
Remove chunks of brick by hand. Brush off any remaining brick pieces, and dust when finished. Make sure the work area is clean before placing new bricks in the space.
Slather a layer of mortar in the empty space with a trowel. Place mortar on all sides of the empty space.
Place the new bricks in the empty space. Press firmly against the mortar and allow the mortar to set for several hours. Clean off any excess mortar with a clean rag.
Put blue painter's tape around the work area to ensure the paint does not bleed to outside areas.
Paint the new area with paint that matches the rest of the brick work. Use a paint brush for smaller jobs and a paint roller for larger jobs. When using a brush, stroke in the same direction. Move paint rollers in a "W" motion to paint evenly over the work area.
Inspect the paint work to ensure you didn't miss any spots. Fill in any missed areas with a paint brush.