Protect the adjacent surfaces by taping plastic sheeting over any wood or metal. Wood and metal surfaces can be damaged by the acid used in cleaning the brick.
Put on safety goggles and rubber gloves. Mix muriatic acid with water in a plastic or rubber bucket. Mix 1 part acid with 19 parts water to yield a 5-percent acid solution. Mix 1 part acid with 9 parts water to yield a 10-percent acid solution. Never use a mixture stronger than 10 percent when cleaning cement or bricks. The acid reacts with the water, so add the acid to the water slowly while stirring with a nonmetallic tool.
Spray the cement-overspray area of the brick wall with water. Soak the area thoroughly to fill the pores of the brick with water. This prevents the acid from entering the pores of the brick, where it could cause damage.
Brush the cement overspray with a stiff-bristled brush soaked in the acid solution. Brush the areas with the overspray vigorously, monitoring the progress of removing the cement. Work a small section until it is clean before moving on to the next section. Avoid scrubbing the acid into the mortar seams of the bricks. The acid will damage the mortar.
Rinse the acid-cleaned brick with water. Hose the area down. This also dilutes the waste cleaning water accumulating at the bottom of the brick wall.