For heavier stains, take three or four cakes of Ivory soap, cut them up and disolve in hot water until you have a "slurp."
Paint this on the marble and let it sit for five days or so. If the gunk starts to dry during that time, consider slopping some more on -- or wetting it down.At the end of the period, hose and wash it all off. Presto, the marble is as good as new!
Thanks to Carolyn for submitting this household hint!