Determine the cause of the dampness in the drywall. If it's wet because there's a leak in the ceiling or behind the wall, repair this first before continuing.
Dry the surface. If just a small area of the drywall is wet, use a hair dryer or heat lamp to dry it out. For larger areas, you may need to set up a space heater or run a dehumidifier to allow plenty of ventilation to dry it out.
Check the drywall for excess dampness by gently running a putty knife or your fingernail over it. If it dents easily or feels damp, allow more drying time. Dry drywall will be hard and not easily gouged or dented.
Remove old paint with a 3-inch chisel-edged paint scraper by working it under loose edges and pushing the paint away from the wall. Work carefully to minimize damaging the underlying drywall.
Sand the drywall smooth with a sanding pad or drywall sander once you've removed as much of the old paint as possible. You may have to do some repairs with joint compound first if the drywall got damaged by water or from the paint removal.