Spanish and Aztec

Mexico conquest started with the search for gold on the mainland with Cortés going from Veracruz to Tenochtitlan (Aztec capital). The Aztecs kicked Cortés and his 450 men out of Tenochtitlan but Cortés put a siege on the city and starved them into surrender (1519-1521).
The Spanish had steel swords, muskets, cannons, and horses which gave them an advantage but they were vastly outnumbered with the Aztecs having 21 million people so the Spanish formed alliances with people who hated the Mexica.
Epidemic disease (smallpox) also aided Spanish efforts by killing tens of thousands of people. Smallpox went through Mexico and killed so many people that the Aztec society couldn't function.