[header] How to clean brick wall [title] Brush the wall with a broom. [step] Use the bristles of the broom to dislodge loose dust, dirt, cobwebs and other debris that's built up on the surface of the brick. Be sure to reach up to the top of the wall and into any corners or crevices that might be hiding dirt. 
[substeps] Brush horizontally away from yourself rather than straight down to keep from covering yourself in dust. An occasional sweeping will usually be enough to keep brick walls looking good between more detailed cleanings.