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 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.