How you approach cleaning brickwork depends a lot on how dirty the brick is. If the brickwork is indoors, cleaned regularly and is marred by only a thin layer of grime, chemical cleaning should do the trick. If it hasn't been cleaned in years, is heavily soiled and is on the exterior of your home, you may need to resort to power washing.
Cover any outdoor plants with plastic sheeting. If you're indoors, protect floors and baseboards with plastic sheeting.
Wet exterior walls with a garden hose. Spray interior walls with water from a spray bottle.
Mix 1 cup of bleach with 1 gallon of water. Wear chemical resistant gloves. You can substitute commercial brick cleaners available at home centers and hardware stores. Do not use unbuffered muriatic acid solutions.
Wet a stiff wire brush in the bleach solution and thoroughly scrub the bricks. Work from the top down. All the mixture to sit on the brick for five minutes.
Rinse the bricks with clean water from the top down. Exterior brick can be rinsed with a garden hose. For interior brick, fill a bucket with clean water and sponge the brick off, changing the water in the bucket frequently.
Repeat the process until the surface of the brick is clean.
Patch the mortar. A pressure washer can easily force water behind the brick. Allow the new mortar to dry at least a week.
Wet the brick thoroughly. For exterior brick, use a low pressure setting, starting at the bottom.
Apply a detergent made for cleaning brick with the pressure washer on a low pressure setting, working from the bottom to the top. Allow the detergent to sit for about five minutes. The key to cleaning brick is using less pressure and more detergent, so if any areas dry out too quickly, re-wet them with detergent.
Scrub heavily soiled areas with a stiff wire brush or a rotating brush attachment on the pressure washer.
Brick is easily damaged, so attach a low-pressure nozzle and gently rinse the detergent. Work from the top to the bottom.