NavList:

The north and south celestial poles on the Moon are close to the north and south ecliptic poles (those are sometimes labeled on star charts, but you can always find them yourself by figuring out which points are 90° from the ecliptic --which you'll find on nearly every star chart, but if not, plot the Sun's coordinates during the course of one year). There's a "fun" way to find these lunar poles in many desktop planetarium apps like Stellarium. Place your observing location on the Moon (see PS). Then set time on fast forward. Watch the stars move and find the spot that doesn't move. Or, while on the Moon, change your latitude to N/S 90° and look straight up. Or, set the option to display RA/Dec "equatorial" coordinates and just look for the pole. Any of these tricks will show you that the Moon's north celestial pole is on a line from Polaris to Eltanin (the brighter star in the head of Draco) about three-fifths of the way between the two stars starting from Polaris. There's no convenient "north star" on the Moon. Your turn: is there a south star? Anything close?

There's no significant precession/nutation on the Moon since it's tidally locked. There is a very small physical libration of the Moon's axis that you could look for, but it's nothing to worry about.

Celestial navigation on the Moon could be accomplished quickly with commercial off-the-shelf (COTS) hardware. You need a star tracker (common tech today for spacecraft). And you need some accelerometers to determine local vertical. Point the star tracker up. It will quickly, automatically return the standard celestial coordinates of the point that it is looking at based on its internal star database. In this case the coordinates returned are the coordinates of the zenith. After some coordinate rotations, we have local right ascension and declination. Then the RA of the zenith is the local sidereal time (always true), which is LHA Aries for navigators. This can be converted to longitude. And the Dec of the zenith is the latitude (always true). Note that these are "astronomical" latitude and longitude based on the gravitational zenith. Since there is substantial deflection of the zenith on the Moon due to its lumpy gravitational field, those will have to be corrected (by readily-available gravitational data) to get true latitude and longitude.

Satellites work better. From the surface, multiple satellites can be observed both visually and in radio frequencies, and similarly satellites in orbit can look down and see surface landers and rovers visually and in radio frequencies. Much faster and much more accurate than traditional celestial navigation. 

Frank Reed

PS: Download Stellarium at stellarium.org. Launch it and use ctrl-F to find the Moon in the sky. With the Moon selected, hit ctrl-G to jump to the Moon. After landing, use ctrl-F again to find the Earth in the sky. Its motion from the launar surface is interesting and somewhat surprising. It's the inverse of the lunar librations we see from here on terra firma. To see equatorial coordinates in order to find the celestial poles, hit E on the keyboard. And in case, you get stuck, ctrl-Q to quit.