You can find nicotine stains on ceilings after smoking indoors for long periods of time. They are particularly obvious when you move an object planted or nailed to the ceiling or wall, such as a lamp or painting. The nicotine stains emerge as a yellowy, dirty frame around the perimeter of where the object used to be. Sometimes it's impossible to clean them. If the stains have been left on for years and won't budge, you should seal them with an oil-based primer and repaint.
Cover all furniture in the room with old sheets or large pieces of plastic, as the oil could drip from the ceiling. It's also a good idea to lay newspaper on the floor as well, particularly if you have nice hardwood or polished concrete floors.
Reduce dripping by mixing your primer at the right consistency. You can test a small area of the ceiling to see if the primer is well-mixed by applying the primer and seeing if it drips excessively.
Hold the roller and pole at a right angle to the ceiling. Roll oil-based primer directly on the nicotine stains until they are well covered. Expand your strokes from that point outward, covering the rest of the ceiling evenly with primer.
Paint your entire ceiling once the oil-based primer is dry.
If you have an acoustic ceiling, it's too porous for a paint roller. Use a spray version of the oil-based primer and make sure your house is well ventilated.