Navigation Using the Moon To Find South
Because the moon has no light of its own, we can only see it when it reflects the sun’s light. As it orbits the earth on its 28-day circuit, the shape of the reflected light varies according to its position. We say there is a new moon or no moon when it is on the opposite side of the earth from the sun. Then, as it moves away from the earth’s shadow, it begins to reflect light from its right side and waxes to become a full moon before waning, or losing shape, to appear as a sliver on the left side. You can use this information to identify direction.
If the moon rises before the sun has set, the illuminated side will be the west. If the moon rises after midnight, the illuminated side will be the east. This obvious discovery provides us with a rough east-west reference during the night. (Information from: WildernessSurvival.net)
Mentally draw a line that connects the horns of a crescent moon and then extend this line down to the horizon. In northern latitudes this will give an approximate indication of south. It works best when the moon is high in the sky and not too near the horizon, when significant errors are possible.
The information and image above were taken from The Natural Navigator
How it Works
The reason this method works is not very complex. The sun and moon move across the sky in an east-west plane. In other words when they are not aligned (a new moon) then they are roughly either east or west of each other. Since the moon reflects the sun’s light, its bright side will be ‘pointing’ to the direction of the sun, ie. approximately east or west. The line that joins the horns of a crescent moon together is at right-angles to this east/west line and any line that is perpendicular to an east/west line must be a south/north line. This is why it works equally well from southern latitudes, for example in New Zealand it can be used to find north.