Cover and protect the floors of the room before beginning any work. Lay down heavy-duty plastic and tape it down to the floors around the edges of the room.
Remove the cellulose insulation from the ceiling. Go into the attic and scoop it into large trash bags, or knock a hole in the ceiling and push it out through the hole into bags. Removing the insulation before you remove the old ceiling allows you to keep it clean and save it for later reuse.
Remove the flat ceiling. There is no particularly delicate way to do this. Knock a hole in it with a sledghammer, hook the curve of a crowbar into the hole and pull it down. Wear head protection, coveralls, gloves and a dust mask when you do this. It is a messy job.
Clean up all the debris from the ceiling removal to maintain a clean work site.
Decide if you are going to leave the ceiling joists as an exposed feature or remove them. In very old houses, the ceiling joists are sometimes hand-hewn beams which look attractive when left exposed. If you don't want the joists, remove them at the eaves by cutting through the nails that hold them in place with a reciprocating saw. If you have any doubts about the structural effect of what you are doing to your house, consult with a structural engineer to be sure that you are not damaging your house's stability.
Install batt insulation between the rafters of your roof. Be sure to leave air space between the top of the insulation and the bottom of the roofing. This air space is essential to allow air to circulate from the eaves to the roof vent and keep the roof ventilated.
Screw drywall sheets to the underside of the roof rafters. Spackle and tape the joints between the drywall sheets. Spackle over the screw holes.
Sand the spackle until it is smooth using 180 grit sandpaper. Prime the surface of all the drywall. Put on a final coat of white ceiling paint.