Explanation:
Here's a (very) brief summary of the fall of the Aztec empire, after the arrival of Hernando Cortes until the fall of Tenochtitlán (read a biography of Hernan Cortez here):
1519 (March 4): The Spaniards land in what is now Veracruz. The natives greet him with gifts. A contingent from Tenochtitlán also arrives with gifts. Cortes showed force and demonstrated his canons, terrifying the messengers.
Cortes sinks all the ships except one small vessel, and moves to the city-state of Tlaxcala. Generally speaking they begin on friendly terms.
The Spanish went on to Cholula. It's unclear what happened, but in the end many people in the city were killed by the Spanish. Read more about Cholula here.
1519 (Nov 8): Cortes and army arrives at Tenochtitlán, and begin on good terms. However, Cortes takes charge and demands tribute and some Roman Catholic shrines to replace the Aztec gods.
Cortes returns to the coast to defeat a rival Spanish army. The remaining soldiers join him.
The Aztecs revolt, driving the Spanish from the city. Cuitláhuac becomes emperor.
The Spanish go to Tlaxcala and make an alliance with them.
Most Aztec cities are conquered, and a siege of Tenochtitlán begins.
1521 (13 August): The last Aztec emperor, Cuauhtémoc, surrenders to Cortes.
