The process of the moon's changes can be described as follows: The moon orbits the Earth, and as it does so, different parts of it become illuminated by the sun.
Over the course of a month, we see the moon go through different phases, starting with a new moon, which is when the moon is positioned between the Earth and the sun and is not visible to us. As the moon continues to orbit the Earth, more of it becomes illuminated, and we see it grow into a crescent shape. This is known as a waxing crescent.
As the moon continues to move, it becomes a first-quarter moon, then a waxing gibbous, and finally a full moon. After the full moon, the illuminated portion of the moon begins to decrease, leading to a waning gibbous, a third-quarter moon, and finally a waning crescent, until it is back to a new moon.