Wash the mineral specimen with warm water. Not all materials will wash off with water, but always start with the simplest solutions.
Clean the selenite with a soft brush. Do not use metal wire brushes; the metal is harder than the selenite and will scratch the specimen. Using a toothbrush along with warm water and mild soap may remove some surface dirt or oils that have accumulated on the selenite during handling.
Pry loose any larger surface items. Use a wedge-shaped piece of wood or bamboo to attempt to pry foreign materials from the selenite. Wood and bamboo are softer than the selenite and won't scratch the sample.