How fast does the Moon rotate?

The Moon's rotation on its own axis lasts 655.720 hours, equivalent to 27.3217 days, practically the same time it takes to complete one orbit around Earth. That coincidence is not random: the tides Earth raises on the lunar body have slowed its spin until it became locked to its orbital period. The result is synchronous rotation, which keeps the same hemisphere facing us. Earth and the Moon are tidally locked, and their rotations are so synchronized that from the ground we only ever see one side of the satellite.

For someone standing on the surface, the Sun would not rise every 24 hours. The full lighting cycle matches the synodic period of 29.53 days, the same one that governs the phases we observe from Earth: lunar night stretches on for many consecutive Earth days. That rhythm affects any equipment operating there, because solar panels go entire days without receiving light and temperatures swing dramatically between day and night.

If what you're looking for is how fast the Moon moves, rather than how fast it spins on its axis, the figure is different: an average orbital speed of 1.022 km/s around Earth, at an average distance of 384,400 kilometers (238,855 miles). These are two movements that are in principle independent, spinning on its axis and traveling its orbit, which in the Moon's case have been locked together for a very long time by tidal friction.