Final answer:
Approximately 50% of the Moon's surface is lit by the sun at any given time, but due to libration, we can observe up to about 59% over time.
Additionally, earthshine can make the darkened portion visible during crescent phases, and refracted sunlight can illuminate the Moon during a total eclipse.
Step-by-step explanation:
Although not always visible, approximately 50% of the Moon's surface is lit by the sun at any given time. Due to natural phenomena such as libration, we can actually see up to about 59% of the Moon's surface over a period of time as it presents different faces to Earth.
During certain phases like the first quarter phase, exactly half of the Moon's illuminated side is visible from Earth.
Additionally, when we observe a crescent moon, we can sometimes see the rest of the Moon faintly outlined, illuminated not by direct sunlight but by earthshine, which is sunlight reflected off Earth.
Even during a total eclipse, the Moon remains faintly visible, lit by sunlight refracted through Earth's atmosphere.