This stand is cut from natural mineral, so it deserves the same care as other stone objects. The main risks are impact and scratching: if you drop the stand onto a hard floor or knock it against another stone object, the edge or polished top can chip. The practical habit is to place it on a stable, level surface and to move it with two hands or by holding the base, not just by the edge.
For cleaning, a soft dry or slightly damp cloth is usually enough. Dust tends to collect in the recess and on the polished top, so wipe those areas regularly. Avoid abrasive scrubbers, harsh cleaning sprays, and soaking the stand in water for a long time; none of those are needed and could dull the polished surface.
Since the stand is small, it can be knocked off a shelf or windowsill easily. If you display it near a window, make sure it is not partially on the edge or on an uneven cushion. If you do drop it and see a small chip, the stand may still work, but check that it still sits flat; a damaged base will reduce stability.
Store it separately if you keep it in a drawer or box, wrapped in a soft cloth or placed in a compartment so it does not rub against other stones or metal. This is common-sense care for natural mineral products and helps the stand keep its shape and appearance over time.