Tape plastic sheeting over the doors and windows to keep the dust in the repair area.
Put on a respirator mask. Change to a new mask if you find it harder to breathe at any point during the project.
Look for a section of loose skim coat where a piece of the concrete has chipped away. If you cannot find a loose section, start at the very edge of the floor.
Place the blade of a chisel under the skim coat where it meets the concrete slab beneath it. Hold the chisel at a narrow angle to the floor so that the blade pushes forward to sever the connection between the skim coat and concrete, not down to chip the floor. Tap on the hammer to push the chisel forward and lift up a section of concrete. Continue positioning and tapping until all of the skim coat is removed.
Remove large skim coat pieces from the room.
Scour the floor with a wire brush to remove any loose chips.
Attach a metal concrete sanding disc to a floor grinder. Turn the floor grinder on and push and pull it over any chips, dips or uneven spots in the concrete to grind it smooth. Skim coats are often laid over damaged concrete floors. Follow the manufacturer's instructions for the floor grinder's operation.
Sweep the floor twice to remove any fine debris.