Put down drop cloths under the area where you will be working.
Climb up onto a stepladder and begin removing the textured surface by scraping it away with a drywall knife; try to tear away as little of the underlying paper as possible.
Scoop a dollop of joint compound into a mud pan. Begin applying a smooth, thin coat of joint compound along the drywall seams with a joint knife. Press drywall tape along each seam and into the joint compound with the knife. Repeat until you have covered all of the drywall seams, paper tears, holes and divots with joint compound. Allow the mud to dry overnight.
Apply a second coat of joint compound the next day. Allow the second coat to dry overnight.
Apply a final coat of joint compound and allow that coat time to dry.
Sand the dried joint compound with a sanding pole equipped with medium-grit sandpaper until the ceiling is smooth. Spray or roll on a coat of primer and let it dry then paint the ceiling.