It begins with carbon moving from land to the atmosphere. Through combustion, carbon turns to gaseous carbon dioxide. When the atmosphere interacts with the hydrosphere, some of the carbon dioxides dissolves in the water as dissolved carbon dioxide. This can also happen through precipitation. Some of the dissolved carbon dioxides can react with water into carbonic acid.
One way is through the burning of fossil fuels. One of the products of the burning of hydrocarbons is carbon dioxide. Another is clearing of forests. Forests are major carbon sinks since trees sequester carbon dioxide from the atmosphere.