I received, like almost every other schoolkid, the information about the shape of the Earth at school, and accepted it without hesitation.
Then I received information about all the other phenomena where the shape of the Earth plays a part, and even though I did not question the shape of the Earth, I had received most of the relevant evidence before college.
Since I found this forum I decided that I would see the evidence directly, looking for the the best evidence for both a scientist (accepting evidence from other scientists) and for a total paranoid.
For a scientist, the fact that the laws of gravitation have been independently tested in several ways is the best evidence possible. From the Cavendish experiment to the orbits of the planets, gravitation predicts so many different phenomena that it is undeniable.
For the non-scientist, the deluge of photos from space are the best evidence, since it is direct, very difficult to fake, and there are so many photos and videos from so many independent sources, that you cannot just brush them all away without strong evidence.
Finally, I decided to see what evidence is there for a total paranoid, one who will only accept a simple, inexpensive test that requires nobody else to help or interfere. Somebody suggested the azimuth of the sun at dawn on the equinox, and I tested this personally, and posted my results here.
If someone wants to measure an object that is so big that direct observation is impossible, you get unmovable reference points (in this case, the stars and planets) and make measurements against them. In this case, all the measurements that navigators have done for centuries indirectly show the shape of the Earth.