One of the best documented methods for determining the Earth's roundness was first performed (to our knowledge) by the ancient Greeks. This was achieved by comparing the shadows of sticks in different locations. When the sun was directly overhead in one place, the stick there cast no shadow. At the same time in a city around 500 miles north, the stick there did cast a shadow.
If the Earth were flat then both sticks should show the same shadow (or lack of) because they would be positioned at the same angle towards the sun. The ancient Greeks found the shadows were different because the Earth was curved and so the sticks were at different angles. They then used the difference in these angles to calculate the circumference of the Earth. They managed to get it to within 10% of the true value – not bad for around 250 B.C.
Another piece of evidence for a globe is the difference between the night skies in the northern and southern hemispheres. The view is completely different because the Earth beneath you is pointing in a different direction. If the Earth were flat, the view should be the same. This can be made even easier by simply comparing when it is night and day in each country.
You can observe the planets as well. They all rotate, and watching over the course of a few days gives a clear picture they are spherical rather than flat. The chance that most of the planets are spherical but the Earth is flat seems very unlikely.
