Climb a ladder and raise the sheet rock panel up to the ceiling joists, starting in one corner of the room. Have another help you on a separate ladder. Place the sheet rock so that the length of the panel is running perpendicular to the joists. To help hold the sheet rock in the moment as well as over time, squirt construction adhesive on the edge of the joists where you are putting the panel.
Drill drywall screws through the sheet rock about on inch from the edges and into the joist beams. Continue placing the boards up to the ceiling and attaching them until you have covered the entire area. Use a knife to cut the boards to fit if needed. Score the board where it needs to be shortened, then snap it along a flat edge to break off the unwanted portion. Use a knife to cut out holes for light fixtures as well.
Spread a thin layer of drywall mud over the seams and screw heads with a trowel. Press drywall tape into the mud along the seams as you work your way across the ceiling. Go back over the taped areas with another thin coat of mud to cover the tape. Leave this to dry for 24 hours.
Sand the mud surface with a fine sandpaper to remove rough patches and then smooth on a final layer of mud. Make the final layer wider than the previous and feather it out away from the tape so that it works down to the ceiling surface. Let this dry for 24 more hours. Now you can finish the ceiling as you see fit.