The moons day is the same length as the lunar month (27 days 7 hours 43.2min) - that's why it always points the same face toward earth.
This isn't a coincidence, an effect called tidal friction means that gradually the Earth has slowed down the moon's rotation until it is now locked to Earth.
It does rotate a small amount because of small variation in the orbit, you can see this from small changes in the shadows on craters.
Well the lunar month you just record the time that the edge of the moon crosses some distance bright star and then note the next time it crosses it 28days later.
For the day rotation you could measure the angle to the edge of some crater compared to the edge of the moon.