katlaughing's link will tell you most of what you need to know, but I'll kibbitz anyhow.

The Earth's orbit around the Sun defines a plane called the ecliptic. The Moon's orbit around the Earth is almost in the same plane, but not quite: it's tilted by a few degrees. Imagine a dinner table with a dinner plate that has somehow sliced diagonally into the wood, so that half the plate angles up from the table and the other half angles down below. The line where the plane of the Moon's orbit around the earth intersects the Earth's orbit around the Sun is called the line of nodes. If a dark or full moon occurs when the moon is on or very close to one of the nodes, then an eclipse occurs. These conditions recur roughly twice a year (the "eclipse season").

So most of the time the plane defined by the Sun, Earth, and Moon (or, to be classical, Helios, Tellus or Gea, and Selene) doesn't coincide with the ecliptic. Or, put another way, the moon is usually out of the plane of the ecliptic. A dark or full moon under these conditions doesn't create an eclipse.

For the rest, half of every planet, including the Moon, is allways lit by the Sun's light (assuming spherical planets). The line between the lit half and the dark half is the terminator. How much of the lit half of a planet you see depends on where you are in relationship to the planet's lit-up half. So if the moon is on the Earth's dark side, (in "opposition") we see almost the entire lit half of the moon. If the moon is between us and the sun, the lit half is away from us, and we can't detect it in the Sun's glare unless it's in the plane of the ecliptic, in which case an eclipse occurs. If a line from the Sun's center to the Earth's center to the Moon's center forms a 90-degree angle at the Earth's center, the moon is at quadrature. Her lit face contains half of her Earth-ward side, and half of her far side; we see a quarter phase.

I hope I have not confused you too much.

T.