Water dripping from an air conditioning vent has only one cause, but there are several reasons for this happening. The cause is condensation, which occurs only when humid air is in contact with a cold surface. If your air conditioner supply vents are sweating, you have a cold surface (the vent), and near it, you have air with water vapor in it. The threshold for condensation to occur is that the temperature of the cold surface has to be below the dew point of the water vapor in the nearby air.
Now, as for the reasons, we can start with the two big ones. Either the air is too humid (dew point too high) or the supply vent is too cold. That means the fixes are simply reducing the humidity of the air or raising the temperature of the vent, depending on which of the two reasons is causing the problem.
How do you tell which one is the real culprit? The table at left gives the clue.