Headstones usually do not see a lot of cleaning, and after a few decades they can become encrusted with pollution and algae. Whether it be for a family member, a personally revered historical person or just for historical preservation, there are many people who are interested in cleaning headstones. Just a little bit of work can make a beautiful granite memorial look as good as new.
Determine if the stone is safe to clean. If it shows signs of cracking, chipping or flaking, it is probable that cleaning will hasten the decay of the stone.
Take a hose, fill buckets with clean water and saturate the stone with the water. If you cannot run a hose to the headstone, you will need to bring enough buckets of water with you to both cover the stone and to clean it.
Wet the brush with bleach and gently scrub the stone, dunking the brush into the water bucket to rinse it. One bucketful will probably foul before the job is done, so two is a minimum for a normal headstone. Repeat at least twice.
Rinse the headstone to check how the job is progressing. A typical headstone left uncleaned for decades will probably require the clean-rinse cycle of Step 3 and Step 4 repeated at least twice, possibly three times.