PRESENTATION OUTLINE
the new moon occurs when the moon is positioned between the earth and sun. The three objects are in approximate alignment (why "approximate" is explained below). The entire illuminated portion of the moon is on the back side of the moon, the half that we cannot see.
At a full moon, the earth, moon, and sun are in approximate alignment, just as the new moon, but the moon is on the opposite side of the earth, so the entire sunlit part of the moon is facing us. The shadowed portion is entirely hidden from view.
The first quarter and third quarter moons (both often called a "half moon"), happen when the moon is at a 90 degree angle with respect to the earth and sun. So we are seeing exactly half of the moon illuminated and half in shadow.
when the Moon is more than half full, but not quite fully illuminated its referred to as a gibbous moon, when you look at it from the perspective of Earth. The reason the light changes has to do with how the Moon orbits the Earth.
A crescent moon is when the moon is less than halfway illuminated, there's waxing Crescent moon, and waning crescent moon.
The most obvious lunar cycle is the 29.5 day 'synodic' cycle. This is the rhythmical waxing and waning of the Moon's visible aspect marked by the full moon when the Sun and Moon are either side of the Earth (opposition), and new moon when the Sun and Moon are to the same side of the Earth (conjunction or occlusion). The Moon takes 27 days to orbit the Earth but since the sun has moved on by 27 degrees in this time the synodic cycle is 2 days longer.
When the moon orbits the earth it exerts a gravitation pull on the ocean. This pulling effect causes the water to rise or bulge against land masses.
When the moon is in the stages of full and new it is aligned with the sun where the combined gravity causes even higher tides. The reason that the moons gravity doesn't effect us like it does the ocean is that the amount of gravity is based on the size of both masses. The ocean is large and the moon is large. Since we are small, the moons gravitational effect on us is extremely minuscule.
Moon gives off no light of its own but reflects sunlight from its rocky surface. What we call moonshine is actually sunshine reflected by the Moon.