You have certainly heard that "everyone" before Columbus thought the world was flat. This is however not true. It is in fact wildly false. Everyone knew the earth was a globe.
(Well, maybe a few ignorant folks thought it was flat. But no one paying attention thought so.)
The ancient Greeks had known it was a globe. Aristotle in fact had attempted to measure its size and come up with a figure that was a little small but a good guess. It was pretty obvious that it was a globe, after all. The sun and moon and stars were assumed to go around the earth. During an eclipse of the moon, when the earth's shadow moves across it, you see the shadow of a globe. If you watch a ship sail out to sea, it goes "hull down," that is the hull disappears while you can still see the sails, as it goes over the earth's curve.
Medieval people speculated about the people who lived on the other side of the globe. Some thought that down was absolute, so that people on the other side would have trouble not falling off. They were depicted with giant feet and toes, good for holding on.
In addition, since medieval people knew that the climate got colder as you went north and hotter as you went south, they were concerned about how people could survive down in the southern hemisphere, close to the "Hot Pole." But in all this, even though we know better than to think that one could fall off the bottom of the globe, or that there is a Hot Pole, or that the universe revolves around the earth, we can recognize that our ancestors knew they were living on a globe.
So where did the "flat earth" notion come from? From Washington Irving, best known now as the creator of the Headless Horseman of Sleepy Hollow. In a comparable burst of imagination, he write a fictional story about Columbus at the court of Ferdinand and Isabella. In this hilarious (?) and very anti-Spanish story, the Spaniards all believed in 1492 that the earth was flat and warned Columbus he would fall off the edge if he sailed west.
This story made its way into the Big Little Book of Racist Stories for Children (or whatever it was called) during the nineteenth century. Everyone knew it was fiction. But at some point it migrated: out of the storybook and into the history book. Now American children were being taught that Columbus was a great scientific thinker, the only one not to believe in a flat earth. (Interestingly, in Europe, where Washington Irving was never in the school storybooks, no such nonsense was ever taught.)
The real Spanish court of 1492 certainly knew the earth was a globe. They were however concerned that the globe was much too big to get to India by sailing west. (Columbus was claiming he could find a shortcut to India and beat the Portuguese.) They were, in fact, right. But Columbus, using Aristotle's measurements and thinking that, since he would be sailing close to the North Pole, it couldn't really be far at all, set off west. And right about the time he thought he should be reaching India, he bumped into Hispaniola.
The Spanish court immediately recognized that there was a whole continent between the Atlantic and the Pacific, when they'd always assumed it was all ocean all the way. They and the Portuguese divided up the globe between them a few years later. Columbus, however, kept going back again and again, denying that he'd found a New World and thinking the silk and spices had to be there somewhere. He is responsible for us calling native Americans "Indians." (See here for more on Columbus.)
But in none of this, note, was there ever the slightest thought that the earth might be flat.