
First Sign of Problems.
In 1517 a comet fell into the temple of the god of war, catching it on fire. The Lake of Mexico flooded into houses. Fishermen noticed a bird with a mirror on it's face. That mirror depicted men fighting on the backs of deer-like animals. Peasents started panicking and fleeing the city, because they saw these problems as a sign that the kingdom is going to fall.
A woman was heard weeping,"My children, we must flee far away from this city!"
Disease.
The Spaniards arrived in Mexico and brought with them an African slave who had smallpox. An Aztec man caught the disease and spread it throughout the empire. Since nobody knew how to treat the disease it kept spreading. In many cases everybody in a house died and they just demolished the houses over the bodies, because they didn't have time to bury everyone. Twenty-five percent of the empire was lost to smallpox. Both the emperor, Cuatlahuac, and military leaders died from smallpox. No one was ruling the empire.
Sacrifices.
The Aztecs sacrificed hundreds of thousands of people in order to please their god. They sacrificed a lot farmers, craftsmen, and other people that had jobs essential to the success of the empire. Many of the people they sacrificed were from the city of Tlaxcala. That city turned on the Aztecs and joined the Spaniards to fight against the Aztecs.
Spanish Conquest.
The Spanish conquest began in the fall of 1519 when the Spaniards landed in Aztec territory. This war went on untill August 13, 1521. The Spaniards killed over 100,000 of the Aztec soldiers and captured the capital of the Aztec empire, Tenochtitlan which forced the Aztecs to surrender. This became known as the Battle of Tenochtitlan.

More information about the Spanish conquest.