In winter, a ceiling fan should be spinning downward and on low speed. By setting the direction of rotation so that air is drawn upward, a ceiling fan pulls up the colder air below, forcing the warmer air near the ceiling to move down to take its place.
Ceiling fans operate best in rooms with high ceilings to allow air manipulation and energy conservation. The ceiling fan doesn't actually change the temperature of the room. The cooling effect is felt on the body, so leaving the fan on when people are not in the room is a waste of energy. It is important to run the fan at a low speed to minimize the wind chill effect.