The Counterfeit Coin

You are given 12 golden coins, though you know that one of them is a counterfeit. The counterfeit coin can be detected because it does not weigh completely the same the others. But at the moment you don't know which coin it is, nor do you know whether it will be lighter or heavier.

Unfortunately, all you have is a scale of the classical type. It is the kind where there are two balanced dishes. By putting objects in, the scale will indicate that one side is heavier than the other (the dish will hang lower) or that each side weighs the same.

How can you find the counterfeit coin by only weighing three times? And is the coin lighter or heavier than the others?