Cut through any caulk or paint that connects the molding to the wall or ceiling. Use a utility knife to make the cut, but work carefully so you don't damage the crown molding.
Slip a small putty knife beneath the crown molding. Lightly pull up on the molding to see if you can loosen it and create a small gap between the wall and the molding. Repeat as necessary. You are not removing the molding at this point, only loosening it. As you do this you may notice the location of the nails that hold the molding in place. Use a pencil to mark the location of each nail.
Place a pry bar under the molding. Do not simply choose a spot and begin prying the wood from the wall. Instead, find the location of a nail and place the pry bar as close to the nail as possible. Set a small wood block under the pry bar where it touches the wall. This will prevent you from damaging the wall as you work. Lift up on the pry bar until the nail comes loose. Repeat with each nail in the molding. The goal is to remove the crown molding by lifting it from the wall one nail at a time.
Remove the entire length of crown molding from the wall. Turn the molding over and gently tap the nails out of the molding with a hammer.
Restore and reinstall.