Watch for the day-and-a-half old moon to appear low in the west shortly after sunset tonight. Binoculars will more clearly show the moon’s complete outline. Direct sunlight illuminates the crescent. Sunlight reflected from Earth faintly lights the rest of the disk. Stellarium
Tonight the crescent moon comes back to the evening sky. You’ll see it low in the west starting about 20-30 minutes after sunset. By tomorrow it will stand further from the sun and higher, making it even easier to spot. On both nights, earthshine will add an extra layer of enjoyment. Use binoculars to see this twice-reflected light best.
The moon orbits once every 27 days during which time its phase changes from crescent to full to crescent again as seen from the Earth. The sun is off to the right in this illustration. ESA
The moon orbits the Earth every 27 days, moving eastward (to the left in the northern hemisphere) at the at about 13° a day, roughly one horizontal, balled fist held at arm’s length against the sky. That’s also the equivalent of one moon-diameter per hour. Its night-to-night motion is easy to see, but hour-to-hour not so much. For that you need a marker ...