Immediately, a takeover of the Aztec government. This was followed by wiedespread disease over the native population, which wiped most of them out. Then came more soldiers and the missionaries from Spain. To the natives, it looked like the Spaniards worshipped a more powerful God, because the Spanish weren't getting sick and dying like they were. It looked like that also to the Spaniards.
Between the combination of European military technology, the spread of disease, and the imposition of the Catholic religion, the native culture was subdued and nearly erased. The Spanish had control of Mexico for 400 years. That is almost twice as long as "The United States of America" has existed as a country. Imagine the impact!