how do people come to an understanding that Earth rotates on its own axis
Answers
The earth rotates about an imaginary line that passes through the North and South Poles of the planet. This line is called the axis of rotation. Earth rotates about this axis once each day (approximately 24 hours). Although you most likely already knew that fact, there is a slight complication most people are not aware of.
More specifically, our rotation period (the time elapsed for one rotation) with respect to the stars is called a sidereal day. A sidereal day is 24 sidereal hours, or 23 hours and 56 minutes on a normal clock. Our clock time is based on the earth's rotation with respect to the sun from solar noon to solar noon. This is a solar day, and it is divided into 24 hours. Because Earth travels about 1 / 365 of the way around the sun during one day, there is a small difference between solar time and sidereal time.