Observing for your self
A simple bit of astronomy and travel can show you the Earth has a curved surface. Spot the pole star in your sky, note where it is in relation to the northern horizon. Travel a fair distance south and make the same observation again and see if it changes. If you are in the northern hemisphere then the the pole star will get closer to the northern horizon and on the equator the pole star will be on the horizon and will disappear over the horizon as you travel further south. This can only happen if the surface of the planet is curved.
And before you ask, yes I have carried out this test when I went on holiday from the UK to Crete a few years ago ago and got a definite change in position of the star patterns. If you accurately measure the angles involved you would be able to calculate using some simple trig the actual diameter of the Earth.