Mudding over painted drywall involves applying joint compound to seal and smooth joints, using materials such as joint compound, tape, and primer. Essential tools include putty knives, sandpaper, a mud pan, a drill with mixing paddle, and a hawk. Techniques include floating (applying the first coat and embedding tape), feathering (smoothing transitions), and sanding (creating a smooth surface). Proper preparation, tool selection, and technique ensure a seamless finish.