Now that we have access to space, the easiest way to prove the Earth is spherical is to leave it and view it from a distance. Astronauts and space probes have done just that. Every picture of Earth ever taken shows only a circular shape, and the only geometric solid which looks like a circle from any direction is a sphere.
There are many ways to prove that earth is round. One of them is observing a ship emerge from a long distance from the sea to the shore. The ship will appear to come up from beneath the water to the surface. This happens because the earth is round. Had it been a flat surface the ship would have sailed straight from the sea to the shore.