The Aztecs went from Aztlan to the Valley of Mexico in the 1200's.
Because of the other groups considering them barbarians, they served as mercenaries for other city-states.
The Aztecs were forced to relocate to different regions in the Valley of Mexico for the next six decades.
Their priests told them they would find a sign from the gods, an eagle eating a serpent on a cactus, that would tell they will build. They found the eagle and decided to settle on an island in Lake Texcoco.
The Aztecs founded their capital city, Tenochtitlan on an island in the Valley of Mexico in 1345.
They built chinampas, causeways, and canals, which gave a path to other city-states.