An ant hill in Argentina
The queen begins the new colony. When she is ready, a queen ant leaves her original colony and sets out to begin a colony of her own. She locates a good spot, maybe under a rock where it is safe and warm, and digs a small chamber. There her eggs will hatch and be the beginning of a new colony.
Many types of ants build their colonies underground, but not all. Some build above-ground mounds, and some build colonies in trees. Some ant colonies are small, and others are huge.
An ant colony can have anywhere from a few ants to millions. Most of the ants in the colony are workers, small female ants that do a variety of jobs to maintain the colony. Some of the workers will care for the baby ants, some will defend the nests, and some will provide and store food. Many of the workers will dig tunnels to build and expand the colony.
Worker ants dig out one tiny bit of dirt or debris at a time, which they carry in their mandibles, jaws that work like little "arms" next to their mouths to carry things. Every bit that they dig out must be removed from the tunnels, and so they carry each piece to the opening of the colony and deposit it outside. This creates the ant hills that we often see above ground.