Scrub any broken areas with a grease-cutting cleanser, to ensure a clean bond.
Place small fragments of soapstone on a solid work surface, and gently break them into a powder with a hammer.
Mix a small amount of clear epoxy on a paper plate or other disposable surface. Brush it over the edges of the broken area, both on the sink and the broken-off piece.
Replace the broken portion of soapstone to its original position and clamp it in place until the epoxy dries. Mix the powdered scraps of soapstone into the remaining epoxy and use that to seal any visible cracks or chips. Allow the epoxy to dry for the amount of time specified on the label.
Use fine, 300 to 400 grit sandpaper to smooth the repaired area until it matches the surface of the soapstone.
Scrape off any crumbling, moldy or deteriorated caulking from the sink's seams.
Scrub the corners clean with a brush and gentle cleanser. Then rinse and dry them thoroughly.
Re-caulk the seams with clear silicone or a color-matched caulking compound. Apply a thin, even bead of caulk along the seam, press it in with your fingertip and wipe away the excess with a soft cloth.
Sand any areas of the sink that have stains on the surface. Start with sandpaper no coarser than 220 grit, then progress to 300 or 400 grit, and finish with 600 grit for buffing.
Wash the sink with clean water and gentle cleanser to remove any oil or film.
Moisten a clean, lint-free cloth with mineral oil. Wipe the sink's inner and outer surfaces evenly with the oil, then use a dry cloth to wipe away any excess.