Scrub the walls with pure white vinegar. Use a stiff brush to apply the vinegar, which will dissolve the mineral content of the white powder on the wall.
Rinse the vinegar mixture off the walls. Use a power washer or simply wash with a brush and clear water. Use a shop vac to remove the water as it accumulates on the floor of the basement. Small amounts of water can also be absorbed with a sponge or towel and wrung into a bucket for removal. Avoid prolonged moisture exposure in the basement to avoid mold growth.
Seal the concrete walls of the basement. Apply the commercial concrete sealer with a brush, roller or sprayer. Allow the sealer to dry according to manufacturer's instructions. Paint the sealed concrete wall, if desired, with standard interior paints.
Remove wet porous materials from the basement and dispose of properly. This includes wet carpeting, wood and plaster wall materials or wet acoustical ceiling material.
Clean non-porous surfaces, such as the cement basement walls themselves, with a mixture of 10 percent bleach and 90 percent water. Wear rubber gloves while applying the bleach mixture with a scrub brush or mop. Allow the bleach mix to remain on the walls at least 10 minutes.
Remove the liquid used during the cleaning process with a shop vac. Alternatively, use a sponge or towel to absorb the water and wring it into a bucket for removal.