My young son recently discovered the Moon and is fascinated by it, repeatedly talking about it and looking for it and pointing at it when he sees it. I'm envious of the wonder he must feel for the mysterious light in the night sky, although I still find it mysterious and marvelous.
When I was a boy scout we were taught how to navigate by the stars, how to find Polaris, the North Star, by imagining a line from the front of the Big Dipper.
Polaris is almost directly "above" the Earth's axis of rotation, and appears to barely move in relation to the Earth. So if you can find Polaris you have a fixed point to navigate from. Even if you don't know where your destination is in terms of cardinal directions, having a fixed point allows you to walk without going in circles.
But if the night is even a little cloudy, you probably won't be able to see Polaris and will be stuck.
Navigating by the Moon is the only practical option in this case. I don't recall ever being taught how to navigate by the Moon, but it's not very difficult.
The basic concept is that the visible part of the Moon, the light part, is facing the Sun, so by seeing how much of the Moon is illuminated and where it is in the night sky you can tell where the Sun is, which will tell you where East or West is and even roughly what time it is.
• Crescent Moon This is the easiest time to guess the time and your general direction. The thinner the crescent, the closer the Moon is to the Sun (from our perspective on Earth). So if you see a thin crescent near the horizon, you are either facing East and the Sun is about to rise or you are facing West and the Sun has just set.
Even if the crescent is not near the horizon, the light part of the Moon always points toward the Sun. The way I'll explain it to my son when he's older is to imagine that the crescent is a bow and an arrow points at the Sun.
The crescent Moon always directs you toward the recently-set or soon-to-rise Sun, which tells you where East or West is.
• Half Moon The Half Moon is always 6 hours before or after the Sun. It is at it's peak at sunset and sunrise.
• Gibbous Moon It can be harder to identify the position of the Moon as it fills out, but the idea of the Moon as a bow still holds. The difference is that a crescent Moon is very near the Sun while a gibbous Moon is more on the opposite side of the sky.
• Full Moon - The Full Moon is completely illuminated by the Sun, which means that the Earth is between the Moon and the Sun, which means that the Moon's position is around 12 hours offset from the Sun's. If you see the Full Moon on the horizon then you are either facing East and the Sun just set in the West (if the Sun hasn't set yet then you should already know where West is) or you are facing West and the Sun is about to rise in the East.
If you see the Full Moon and it's not near the horizon, you may be able to tell North and South from the pattern of craters.
The darker craters are in the northern part of the Moon's face and the lighter areas are in the south.
If you can't make out the details of the Moon's face, you should still be able to tell which half of the sky the Moon is in. Unless you're near the equator, the Moon will be in the southern half of the sky. This is especially true in Winter (the reverse being true in the Earth's southern hemisphere.)
• No/New Moon - Well, in this case you're stuck, but this is only couple days each month