Remove the furniture from the room. Cover the floor with tarps.
Scrape off what's left of the old texture, using a wide drywall knife. Run a hand sander over the ceiling to get it smooth and flat.
Cover the ceiling in primer, starting around the perimeter with a paintbrush and proceeding to the rest of the ceiling with a roller. Cover the surface completely, but keep it flat and smooth. Let it set for 12 hours.
Brush textured paint onto the ceiling along one edge, covering about 4 feet. Use a roller to apply more of the textured paint out over the surface, as far as you can reach from one position. Work the paint with the roller to get a consistent texture to the surface.
Move the ladder and apply textured paint to the next section in the same manner. Repeat this process, covering the whole ceiling section by section. Step back frequently and assess the entire textured area to make sure the texture is consistent throughout.
Let the textured paint dry for 24 hours before moving the furniture back into the room.