Vacuum and dust the basement thoroughly. Rent a dehumidifier and run it in your basement. Allow the dehumidifier to complete several cycles. Allow it to run for at least two full days, or even longer, if you have an especially damp basement.
Put on goggles and a dust mask, and scrape off any loose or crackling paint from the your basement walls. Pour a waterproofing paint into a paint roller pan. The waterproofing paint should be the same type as the paint you just scraped off. For example, if the paint you scraped off was latex-based, your waterproofing paint should also be latex-based.
Apply the waterproofing paint with even, bold strokes. Allow the paint to air-dry for at least a full 24 hours. Apply a second coat, allowing it a full day to dry as well. These two coats will ensure that your basement walls are properly sealed.