Fact 1: no flat-earth theory stands up to scientific examination
Fact 2: the earth is 100% certainly a sphere (well, oblate spheroid in reality).
Let's look at some common arguments proving beyond doubt that the earth is not flat:
1. There is no feasible way to explain our observations of the sun in a flat-earth model. Firstly, the sun would start small, grow larger, and then get smaller again every single day as it passes overhead. In addition, if it travels at a constant speed over the whole disc-shaped earth, it would appear to speed up as it passed overhead then slow down again as it moves away (in the same way, if you watch a fast car drive past, your head turns fastest at its nearest point). Finally, there could be no seasons in the way we observe them - for the sun to make a full circle of the flat-earth in one day, it would have to move faster then further away it got from the us (in winter) as it has a bigger circle to move around.
2. Nobody has ever found the edge. People have circumnavigated the globe, fully crossed both the Arctic and Antarctic and explored pretty much every square inch of the earth, but nobody ever found the edge.
3. Direct intercontinental flights south of the equator would be impossible. Flying from, say, Australia to South Africa would be well beyond the range of a commercial aircraft, yet go an look on Expedia - they happen every day.
4. There are photos of the curvature of the earth from high altitudes, near space, Earth's orbit and outer space. They all show a spherical rotating ball. Every single one. That's a huge conspiracy, and some pretty advanced CGI if it were all faked.
5. The ship-going-over-the-horizon argument, which is demonstrated even better if two people watch it from different heights (such as the bottom and the top of a cliff - the person at the bottom loses sight much earlier than the person at the top).
6. We know exactly what is the structure of the earth from its surface to its core, and can measure (and predict) seismic waves coming from an earthquake one side of the earth using sensors on the opposite side of the globe.
7. The shadow of the Earth during an eclipse is round, every single time. The very fact that there can be lunar eclipses proves that the sun and moon must be on different sides of the Earth, which can only be the case if the Earth is a sphere.
