You may find it easier to check some of this if you have a box fan handy. Box fans usually follow the right hand rule as well.You don't feel a breeze, 2 but it circulates warm air from the ceiling towards the walls and down towards the floor. In cold weather, you set the fan so that it pushes air up into the ceiling. This causes you to feel a breeze, which cools you. In warm weather, you set the fan so that it pushes air down towards the floor. Vazquez-Abreams mentions using a pull chain in a comment to another answer. The fans in my house have a small black switch that slides up and down. Many (most?) modern ceiling fans provide some mechanism to do this. Once you have set the direction of the pitch of the blades, you can reverse the airflow by reversing the direction the fan spins. You can make it follow a left hand rule by reversing the pitch of the blades. 1 When it's pushing air down on you, it will then be spinning in a counter clockwise direction as you look up at it.
The usual convention is given by the right hand rule: if you hold your right hand so that you can curl your fingers in the direction the fan is spinning, then it will push air in the direction that your thumb is pointing. Which direction it pushes air is determined by the direction the fan is spinning, and the direction the blades are pitched. As a result, when the fan spins, the blades push air either up towards the ceiling or down towards the floor. The blades of a ceiling fan are pitched out of plane slightly.
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