Tip: Using flat ceiling paint will greatly minimize the appearance of surface imperfections.
1.Use a stud finder to find the ceiling joists and make pencil marks on the wall. This will guide you in lining up the sheetrock and attaching it to the ceiling.
2.Buy 3/8" or 1/2" sheetrock, enough for the job. Sheetrock comes in several thicknesses. The thinner pieces are most suitable for going over existing drywall and won't add too much weight to the ceiling.
3.You will need help installing the sheetrock on the ceiling. If you can't find anyone to help you, rent a drywall jack at any rental yard or home store. This is a simple hydraulic lift that maneuvers and holds the sheetrock into place while you install it. When hanging the sheets, stagger the seams and avoid having four corners butting together, as this creates a weak joint that will crack later.
4.Use drywall screws instead of nails....
Note: I have popcorn ceilings throughout my town home, never liked them but now I am use to them...I don't look up much :). A few years ago I had a leak from my washing machine causing damage to the unit below me. I hired a handy man to fix it and while repairing the damage he painted over the existing popcorn making their whole bathroom ceiling smooth.