There is a small amount of sulfur in coal. When the coal is burned, the sulfur enters the atmosphere as SO₂ and SO₃ gas. This gas reacts with water vapor to make sulfuric acids. The size of the droplets are VERY, VERY tiny and they get carried into the atmosphere to high levels, where the acid droplets can move for thousands of miles from the smoke stacks. These droplets dissolve in rain water and lower the pH to make acid rain.

Acid rain happens because of chemicals in the air combining with water to create acids. The most common is carbon dioxide, which makes carbonic acid with rainwater in the atmosphere. This is entirely natural. Fortunately, carbonic acid is such a weak acid that it doesn't do any real damage. Pollution and volcanic eruptions often put sulfur trioxide in the atmosphere, which becomes sulfuric acid in combination with water, which is a very strong acid and causes quite a lot of damage when it happens. Nitrogen-rich pollution can also give rise to nitric acid, which is also strong (and bad).