How to navigate with possible maximal precision using moon phases?

The Moon is the brightest celestial body seen in the night sky, and it is possible to find even through moderate clouds. So it's a good natural object to use in navigation when a compass is not available.

A full Moon is quite an easy case - it's directly on the opposite site from the Sun. However, in the other phases, are there tables or mnemotechnical methods allowing to determine the north based on moon shape, assuming the time is known? Are they different depending on geographical height? Is it possible to estimate both north and the time of the night, when only the geographical height is known?

-
Google gives some suggestions: google.com/search?q=finding+north+using+the+moon – barrycarter Dec 28 '15 at 5:28

In other phases, the angular distance of Sun from Moon is equal to the phase of the moon, in the direction of the lit side. One of the methods could be to estimate the position of Sun based on this, and then you can, assuming time is known, estimate North

If you don't know time, use constellations(which can form a seperate question) to estimate North and the reverse of above method for time.

Now, if there are clouds and you cannot see any constellations, well, you need to be able to calculate cosines and sines and their inverse in your heads. This method, which I will not describe depends on the rate of change of moon's position, which you'll have to estimate using your hands.

EDIT : I will have to search for my notes for actual calculation of time, let's see if someone else answers it. But let me tell you how to find direction just using Moon, though this is less accurate than if you already know the time.

From the center of the Moon, draw a line in the sky and follow it towards the lit side of the Moon, the spot where it cuts on the Horizon is either East or West. It is East if you are observing this in Waning Phase i.e. after a Full Moon, else it is West(if after the days of a New Moon). You can get the rest of the directions this way.

Here's how it works. The line you just drew was approximately the ecliptic, the apparent path of Sun in sky, it is at an angle of 23.5° from the equator, so that is the maximum inaccuracy that you might have for your cardinal directions. This would actually lead you off in a wrong direction initially, but the ecliptic keeps on moving, so keep on doing this for the whole night, the positions of your North will be varying but the averaged out value will be better than your initial value.

-