How does water move throughout plants?
Most water moves up through the xylem by capillary action. Imagine dipping a pipette into a small pool of water; the water would rush up into the pipette. Or, imagine dipping the edge of a paper towel in water. The water "runs" up the paper towel. This is capillary action.

As water evaporates out of the leaves and such in higher regions of the plant, a capillary force pulls up more water. If for instance, you were to dry the top of your saturated paper towel, more water would be pulled up from the pool below to wet that top section.

As for a molecular explanation, Wikipedia has a good explanation of Cohesion-tension theory.