In olden days people felt that earth is flat because it looks flat. However they had a doubt, if it is flat how does the water in ocean remain there, Why does it not spell out of the earth ? To get clarity they assumed fencing around flat earth. After that,

1. they assumed shape of earth is round by observing the shadow of earth in lunar eclipse. In every eclipse they found the shape of the earth is in round even though there is a chance of getting linear, elliptical shadows by a circular object. 

2. some sailors who started their journey in ocean, reached the same place after travelling large distance in one direction only. 

3. observing ships approaching the port also helped to change their opinion about the shape of the earth, that is, usually they see smoke of the ship first and then top of the ship after that the whole ship.

4. observations about the movement of stars. Different stars visible from different places on the earth also helped to think about the shape of the earth. 

5. in 1969 when man landed on the moon and observed the earth’s shape from the moon and it is spherical.