Rotation of Moon.. The fact that we always see the same side of Moon means that it *must* rotate on its axis once for every orbit around the Earth. If the Moon did NOT rotate (spin on its axis) then we would see both sides as it orbited Earth. This is called synchronous rotation and is due to tidal locking. The time for the Moon to go through one cycle of phases (from full back to full or new back to new) is aboout 29.5 (Earth) days. Thus, a "day" on the Moon is equal to 29.5 Earth days, which is also the time it takes for the Moon to orbit (revolve around) the Earth.
Phases of Moon. This diagram is what you would see if you could look down on the Earth-Moon system from a large distance. Note that half of the Moon and half of the Earth (the halves facing the Sun) are light colored (these parts of the bodies would be in sunlight, while the other halves are in darkness. You must "put yourself in the picture" to see what you would see STANDING ON THE EARTH. For example, if the Moon were on the left hand side of the diagram ("Full") then if you were standing on the Earth at the point labeled "sunset", what would you see? You would see the Sun off to the right, setting in the west as the Earth turned (couterclockwise as shown by arrow on Earth), and the Moon would be opposite the Sun, on the eastern horizon, rising as the Sun was setting. So the full moon always rises at sunset.
Phases in a room. You could demonstrate the idea behind the phases of the Moon in a room. Here the illumination is provided by a lamp off to the right. The Earth (position of observer) is the guy in the chair. The Moon is represented by the orange ball held by the woman. By moving the ball around the guy in the center, mimicing the motion of the Moon around the Earth, the ball would go through "phases". The important thing is the relative position or angle between direction of illumination, observer and ball.
Synodic and sidereal months. Relative to a fixed coordinate system , the Moon orbits the Earth in one sidereal month (sidereal= "relative to stars"), which is equal to 27.32 days. However, the time between full moons (or new moons) is a time period called the synodic month (29.53 days).