Hammer in any nails that have popped out so the heads sit flush in the drywall boards. If screws were used, drive in any that protrude from the drywall.
Sand the original skim coat until it's smooth and any roughness or uneven areas are removed. Use 150 fine-grit sandpaper in a drywall sander, which is a sandpaper pad with a connected handle. Use light pressure to sand, otherwise you may sand into the drywall paper beneath the mud.
Vacuum over the walls and along the baseboards with a shop vacuum to remove any drywall dust left behind after sanding.
Mix a box of drywall mud with 1 to 2 cups of water in 5-gallon bucket. Use a stirring attachment on an electric drill for even mixing. Mud with the proper consistency is thin enough to spread on easily but is not runny.
Scoop some mud onto the drywall knife, which resembles a wide metal blade with a handle attached. Smooth the mud onto the drywall, holding the knife at a 45-degree angle to the wall. Smooth on a thin coat of mud, spreading it in one even stroke. Continue scooping and smoothing on mud until the wall is covered in a thin coat.
Allow the refloated coat to dry for 12 hours. Sand it and check that all the seams are now sitting flush and no imperfections show. If the seams still appear sunken, apply a second coat of mud before texturing and painting the wall.