On its web site, the Association for Gravestone Studies in the United States has posted helpful information on cleaning, clearing, re-setting and maintaining gravestones and cemeteries.
Though an international organization, the Association is largely directed to the study of historic cemeteries in the United States, and some of the information on preservation and conservation is specific to the United States (for example, brand names of cleaning products).
Still, the general information and tips are very useful. You can find a range of information in the FAQ as well as in the list of downloadable files in the Knowledge Center.
One piece of advice given on the site FAQ is NOT to use shaving cream to highlight inscriptions in order to read them.
Our professional conservators tell us it is definitely not a good idea to use shaving cream on porous gravestones because there are chemicals and greasy emollients in shaving cream that are sticky and very difficult to remove from the stone with a simple washing. Indeed, even with vigorous scrubbing and lots of rinsing, the cream fills in the pores of a porous stone and cannot all be removed. The result of leaving it there is that in time it may discolor or damage the stone.
Instead, use a mirror to shine sunlight across the face of a stone, making the lettering stand out. You should always prefer a non-invasive method to interact with gravestones just as we do with medical tests on our own bodies.