Different molecules stick together into a solid because there is a certain amount of attractive force between them. To break them apart, you must exert enough energy to overcome this force. As a metaphor, imagine pulling on a rubber band. If you only pull a little, the rubber band snaps back, but if you pull hard enough it will break.
You mentioned vaporizing water. The kind of energy we put into water to vaporize it (a.k.a. boil it) is heat energy. What we call "heat" is a shorthand for how tiny particles vibrate or move around and bounce off each other. If you put a cold object next to a hot object, the molecules from the hot object bump into the molecules of the cold object, transferring some of their energy and making the cold object's molecules vibrate more. Seeing this, we say that the heat is flowing from the hot object into the cold object. We can also transfer heat energy without physical contact: a hot object shoots out some of its energy as electromagnetic radiation (visible light, infrared, etc.), and a cold object absorbs it.
The point is that once a molecule is vibrating fast enough, the intermolecular forces can't hold it any longer—the rubber band snaps, so to speak—and it flies off. The water boils.
What does this mean for your theoretical "molecule-shifter"? Well, you could say that their real power is the power to control heat. Maybe they have to obey most of the laws of physics, and so they have to "spend" a certain amount of their own personal energy to make an object hotter, or suck heat out of one object before they can pour it into another. Or maybe they can tap into some other source of energy like <insert hand-wave here> that allows them to do as much heating as they want. It's up to you.
(P.S. I've been talking mostly about heating or vaporizing objects. Cooling or solidifying them is just the same process in reverse: a particle loses energy and moves slower until it is slow enough to get trapped by those intermolecular forces. Also I didn't talk much about the solid-to-liquid transition: a liquid is a state where the particles have enough energy to leave their fixed position and start sliding around past all their neighbors, but not enough energy to fly off somewhere.)