The Full Moon Gives Directional Information
The moon is full only one day each month. At this time, it rises in an easterly direction (which can vary quite a bit) at about sunset, crosses your meridian (that is, it bears 180 degrees True in the Northern Hemisphere or 360 degrees True in the Southern Hemisphere) at solar midnight (12 hours past Local Apparent Noon), and sets in a westerly direction (which can also vary quite a bit) around sunrise.
The full moon's maximum altitude for any given night is not nearly as predictable to a navigator in the field as is the sun's maximum altitude for any given day. The sun's maximum altitude is tied to the four seasons, while the moon's maximum altitude--as best as I can tell--is based on some squirrely factors we don't need to understand for our purposes.
Full Moon's Altitude No Greater Than 45 Degrees
If the full moon's altitude at solar midnight does not exceed about 45 degrees from the horizon (in other words, if it's no more than halfway up the sky), and if you know the time, you can use the moon as a compass in the same way you can use the sun as a compass when its maximum altitude (its altitude at Local Apparent Noon) doesn't exceed the same number--45--of degrees.
Since the Northern Hemisphere's full moon bears due south at solar midnight, and since it travels across the sky at 15 degrees per hour (360 degrees in a full circle divided by 24 hours in a day = 15 degrees per hour), then one hour after solar midnight a low-hanging full moon will bear near 195 degrees. Two hours after solar midnight, it will bear around 210 degrees. Three hours after solar midnight, it will bear around 225 degrees, and so on until it goes on to set in a westerly direction.
Conversely, after rising in an easterly direction, the full moon travels toward the meridian. Three hours before solar midnight, a low-hanging full moon will bear about 135 degrees. Two hours before solar midnight, it will bear near 150 degrees. And an hour before solar midnight, and it will bear 165. Of course, at solar midnight, it will bear 180 degrees.
Things are turned around in the Southern Hemisphere where the full moon still rises in an easterly direction and sets in a westerly direction, but instead of arcing across the southern sky, it arcs across the northern sky (as does the sun), crossing due North at solar midnight.
In the Southern Hemisphere then, one hour after solar midnight, the full moon will bear about 15 degrees to the west of due north, or around 345 degrees. Two hours after solar midnight, it will bear around 330 degrees. Three hours after solar midnight, it will bear around 315 degrees.
Three hours before solar midnight, the Southern Hemisphere's full moon will bear about 045 degrees; two hours before, about 030 degrees; and three hours before, about 015 degrees.
Full Moon's Altitude Greater Than 45 Degrees
If the moon's altitude with respect to the horizon is substantially greater than 45 degrees at solar midnight, you can still rely on the fact the the full moon rises in at least a somewhat easterly direction, crosses your meridian (bears 180 degrees in the Northern Hemisphere, or 000 degrees in the Southern Hemisphere) at solar midnight , and sets in an least a somewhat westerly direction. What you can't do is use the "high-flying" moon's position at other times of the night to accurately project a bearing down to the horizon. The reason for this is that when the moon is too high in the sky its 15-degree-per-hour travel across the sky does not sufficiently correlate to its bearing change, as that bearing is projected down to the horizon.
Directions by a Near Full Moon
As mentioned earlier, the moon when full crosses the meridian at solar midnight. One day before the full moon, the moon crosses the meridian an hour earlier. Two days before a full moon, the moon crosses the meridian two hours earlier than solar midnight.
One day after the moon is full, it crosses the meridian one hour after midnight. Two days after the full moon, it crosses the meridian two hours after midnight.
Of course, the big trick here is determining how many days you are away from a full moon. With some observation and practice, you might get pretty good at guessing. While these directions might not be accurate to within 20 degrees, you can still determine a general direction in which to proceed to a baseline.
If the near-full waxing or waning moon rises no higher than 45 degrees on any given night, you can use it as a compass, provided you have a timepiece.