How do I prevent water from leaking through the baseboard edges and down onto the first floor. There is a small space between the tile floor and the wall.

The best way is to seal this space with silicone or acrylic caulking. Run a bead around the perimeter of the base. When you are done with the job the caulking should easily peel off or you can leave it in place.

CAUTION If you use silicone caulking you will need to wait 24 hours for the caulking to cure. Also be careful that the silicone does not bleed into the marble and discolor it. Use a clear silicone.