Of all heavenly bodies, the Moon is perhaps the most fun to observe with the naked eye thanks to the fact that it changes phases and because one can actually see surface features without optical aid.
When it comes to Moon's phases, they are actually very easy to explain. Although it may not always appear so to us, the Moon is always half lit. What we can see and when we can see it depends on where the Moon is in its orbit relative to the observer. To explain what is happening, let’s take a trip around the Earth by way of the Moon. A total orbit of the Moon around the Earth takes about 29 days. At new Moon, the alignment is Sun, Moon, and Earth in that order and in a straight line. From the Earth, the Moon is lost in the glare of the Sun, hence why we cannot see it. As the days progress, the Moon will move out of the Sun’s glare and the Sun will set before the Moon. In the days just after new Moon, from the Earth, we will begin to see a tiny bit of the lit side of the Moon just after sunset.
As the days progress, we will continue to see more of the lit side of the Moon as our cosmic companion distances itself from the Sun’s glare. As the Moon moves from new to first quarter, it is called a waxing crescent. At first quarter, the point in its orbit where the Moon has gone a quarter of the way around the Earth, the Sun, Earth, and Moon form a 90 degree angle, with Earth serving as the right angle of an imaginary cosmic triangle. Because of this 90 degree angle, the Moon appears half lit to us on Earth because we see exactly half of its lit side. At first quarter, the Moon also rises exactly half way between sunrise and sunset.
As the moon continues in its orbit from First Quarter, it is now farther from the Sun than the Earth. After the angle to the Moon relative to the Earth is over 90 degrees, we see more than half of the lit side of the Moon and the Moon continues to rise later each night. At this point of being over half full, the Moon is now called a waxing gibbous.
At full Moon, the Sun, Earth, and Moon are all in a straight line relative to each other. The Moon is now appears full as we can see the entire lit side because it is directly opposite the Sun in the sky. After full Moon, the Moon continues its orbit, now traveling back toward the sun as a waning gibbous. We see less and less of the lit side of the Moon as it returns toward the Sun. At third quarter, when the Moon reaches a 270 degree angle from the Sun, we again see half of the lit side and half of the dark side. The Moon now rises exactly between sunset and sunrise. After third quarter, the Moon now moves even closer to the Sun as a waning crescent, rising later each day until it is again lost in the glare of the Sun as a new Moon.