Over the last six evenings, the waxing crescent moon has grown thicker and has appeared higher above the horizon each evening as it moves away from the sunset. By tomorrow evening, the moon will have waxed to first quarter, passing Mars, Regulus and Saturn as it completes about one-quarter of its lunar month.
The best times to observe the moon with your binoculars or telescope are the days around the first and last quarter moon. Stargazers will find sharp and detailed surface features along the terminator, the line that separates the bright illuminated side from the dark side of the moon. Craters and mountain peaks will cast shadows and stand out because the light from the sun is hitting the lunar surface on an angle.
Contrary to belief, the full moon is the worst phase to observe. Direct rays from the sun cause surface features to be washed out. Only light-colored rayed craters stand out like splashes of white paint when observed with optical aid during the full moon.