The Moon moves about 15 degrees (almost a hand span) across the sky from from night to night. The side of the Moon toward the Sun is lit, so before full moon the left side of the Moon (for Southern hemisphere viewers) is the lit side. The right side of the moon is lit after full moon.
The Moon looks different in the Southern Hemisphere than it does in the Northern Hemisphere. That's because folk in the Northern Hemisphere view the Moon upside down. The following images taken by Maurice Collins show the Moon the way it ought to look, at least for Southern Hemisphere observers. See the bottom of the page for images of (near) new moon, first quarter, full moon and last quarter moon.