Hernan Cortes set sail for the New World from Spain in 1519,
in search of gold and other treasure. He arrived on the
coast of Mexico, then controlled by the Aztec empire.
Cortes founded the city of Veracruz. He gathered an army there,
and then marched on to the Aztec capital city
of Tenochtitlan, where he met with Montezuma, the Aztec
emperor.
Following Aztec religious traditions, Montezuma believed that
Cortes and the other Spaniards were descendants of the god
Quetzalcoatl. Using this to his advantage, Cortes took
Montezuma hostage.
Cortes and his men were forced to flee when the Aztecs
revolted against them, but in 1521 Cortes returned and
conquered the city, and soon all of the Aztec empire. For
the next 300 years, Mexico was a colony of Spain.
You can find the whole story of Cortes and Montezuma in
the book Montezuma and the Aztecs.