How do you measure the distance on a map?

It actually depends on the type of map - but if all distances on the map are supposed to represent equal distances in the real world, you can refer to the legend of the map where there should be a scale indicating the ratio of map distance to actual distance - for example, there might be a line at the bottom that is 1 inch long that is labeled "1 mile" meaning that if 2 points on the map are 3.5 inches apart, they are 3.5 miles apart in the real world.

If the map covers a big enough area however, you run into the problem that you can't perfectly represent a curved surface on a flat map. If the map is for a small enough area, the discrepancy is negligible, but when a map is covering thousands of miles, the discrepancy starts to become noticeable and you have to compensate for it.