Prayer and pointing to Mecca seems pretty simple on the moon - but if Ramadan is based on when you can see the moon, it seems that Ramadan would start as soon as the person in charge walks by a window.
Moon-dwelling Muslims would go by the phases of Earth, if they wanted to match Earth timing but not rely on communication with Earth. The Earth as seen from the Moon exhibits the opposite phase as the reverse. Ramadan would begin when the Moon-dweller sees the Earth as being just past full. If you wanted, you could synch it with a particular timezone on Earth, by watching for when that location on Earth (Mecca or whatever) just rotated past the terminator so it experienced sundown. (Of course none of this can be directly observed if you're on the far side.) (And I get your joke about seeing the moon when you're on it; this is the practical alternative.)
