To clean fireplace brick, acid based cleaners are very effective. There are many acid based cleaners made for this purpose, but one of the more popular choices is muriatic acid. Muriatic acid is available at home improvement stores. You will need to mix it with 9 parts water to 1 part acid. Get the brick wet with water before applying the acid solution. Next, apply the acid solution and scrub the area with a stiff brush. Wipe away the grime, and then rinse the area well. If you are planning on using another type of acid, consult with a brick professional for proper use.