Our Moon's shape doesn't really change — it only appears that way! The “amount” of Moon that we see as we look from Earth changes in a cycle that repeats about once a month (29.5 days). The relative positions of our Sun, Earth, and Moon, cause these changes.
As our Moon orbits around Earth, the side facing the Sun is always illuminated, just like Earth's daylight side is illuminated by the Sun.

What we see from Earth, however, is a different story. Starting with the dark new Moon, we see the light part of the Moon “grow” from a sliver to a half to a full Moon — and then the illuminated part decreases, becoming thinner until there is no visible Moon in the sky and we are at the new Moon part of the cycle again.

We have a “new Moon” when our Moon's orbit around Earth moves it between Earth and the Sun. From Earth, the Moon's surface looks dark because the illuminated side is facing away from Earth. As our Moon continues its orbit counterclockwise around Earth (viewed from above the north pole), more and more of the illuminated part of the Moon becomes visible to us, until it reaches the “full Moon” stage. A full Moon occurs when the Moon has moved in its orbit so that Earth is “between” the Moon and the Sun.

Between the new and full Moon, the amount of Moon we see grows — or waxes from its right side toward its left side. As it passes the full Moon stage, the amount of illumination decreases — or wanes — from right to left. Finally, the Moon returns to its position between the Earth and the Sun, and on Earth we observe the new Moon again.

In the southern hemisphere, illumination of the Moon increases from the left to the right side in the waxing phase and the dark part increases in coverage from left to right in the waning phase, which is opposite of the northern hemisphere. No matter where on Earth an observer is, however, the phases of the Moon occur at the same time.

Formation of a New Moon to Full Moon:

The cycle of the moon's phases is approximately 29.5 days long. During this time, the moon goes through different phases, starting from a new moon and progressing to a full moon. Let's break down the process of the moon's phases in detail:

New Moon:
1. The new moon is the first phase of the moon's cycle.
2. During this phase, the moon is not visible from Earth as it is positioned between the Earth and the Sun.
3. The sunlight falls on the side of the moon that faces away from us, making it appear dark.

Waxing Crescent:
1. After the new moon, the moon starts to move away from the sunlit side, and a small crescent shape becomes visible.
2. This phase is called the waxing crescent, and it occurs within a few days after the new moon.
3. The crescent shape gradually becomes larger, as more of the sunlit side becomes visible.

First Quarter:
1. As the moon continues to move in its orbit, more and more of the sunlit side becomes visible.
2. The first quarter moon appears approximately a week after the new moon.
3. During this phase, exactly half of the moon is illuminated and visible from Earth.

Waxing Gibbous:
1. After the first quarter, the moon continues to wax, meaning it becomes more illuminated.
2. The waxing gibbous phase occurs a few days after the first quarter.
3. The moon appears to be more than half illuminated, but not yet fully lit.

Full Moon:
1. Finally, after approximately two weeks from the new moon, the moon reaches its full phase.
2. The full moon occurs when the entire sunlit side of the moon is visible from Earth.
3. This is the brightest phase of the moon's cycle, and it appears as a complete circle in the night sky.

Conclusion:
The process from a new moon to a full moon takes around 29.5 days to complete. During this time, the moon gradually transitions through different phases, starting from a dark new moon to a fully illuminated full moon. It is important to note that the exact duration may vary slightly due to the moon's elliptical orbit around the Earth.