To properly displace hot air and keep your room at a decent temperature, you should turn your fan in the "reverse" direction. This direction makes the fan spin counterclockwise, blowing air toward the ceiling instead of blowing it toward the floor. The movement displaces heat and allows cold air to blend with warmer air.
If you want a nice cool breeze blowing in your direction, try putting the fan in "forward" mode. This makes the fan spin clockwise, blowing air down to the floor. If you have an air conditioning system with vents on the ceilings of each room, you might experience the cooling effect much faster with a ceiling fan pointing down every time the air conditioner's blower fires up.
Don't set your fan any faster than its lowest speed if you want to displace heat in the winter. Although the fan blows toward the roof, the air won't blend as gradually as it should while the fan blows and, eventually, all you'll feel is a cold draft of air moving in your direction. A lower fan speed allows the air to have time to blend more thoroughly and circulate gently across the room.
Lighter objects tend to have less attraction to the ground than heavier objects. The same rule applies to air, which gets lighter when heated and heavier when cooled. Turning your fan in a forward direction in the summer creates a current of air that gets cooler, since the hot air gets forced to mix with the cooler air below it. The opposite happens in the winter. Warmer air gets displaced from where it sits and comes to the ground after the cool air below it has already blended with it.