The first step in Hernan Cortez' conquest of the Aztecs was actually taken not by Cortez himself, but the then-governor of Cuba--Diego Velásquez. In February 1519, after receiving vague reports of a wealthy civilization in Mexico, Velásquez sent a career soldier--Cortez--to explore the area. Cortez' original orders were for reconaissance, and the only military action he was expected to take was to free any found Christian prisoners. At the last minute, Velásquez was swayed by his advisors, who claimed that Cortez was incapable of leading a major expedition and ordered Cortez to remain in Cuba. Disregarding the order, Cortez sailed from Cuba in February 1519. Soon, Cortez landed in present-day Mexico, and he brought with him about 400 soldiers, 100 sailors, and--most importantly--between 10 and 20 horses.
Cortez landed near Villa Rica de Vera Cruz, and soon gained political control of that city. Once firmly entrenched in power, Cortez renounced the authority of Velásquez and declared himself to be in supreme command. Bold and ambitious, but yet politically aware, Cortez sent a letter to King Charles I of Spain (also known as the Holy Roman Emperor Charles V). In this letter, he proclaimed himself to be a Christian ambassador to the heathen cultures of Mexico, and attempted to prove that he was correct to denounce the authority of Velásquez. Of course, the key element in the letter was the mention of the Aztecs' immense wealth, of which rumors had been widely circulated. Unhappiness and unrest among his force caused Cortez to burn the ships in which the Spaniards had arrived, thus ensuring conquest as the only means of long-term survival.
Not long after the Spaniards began their trek inland, they came upon the Tlaxcalan people. After two weeks of fighting, the Tlaxcalans surrendered (mainly because they resented the power of the Aztecs and the tribute that was required). They became Cortez' most faithful allies. The Tlaxcalans joined the Spanish force, increasing it to several thousand men. By October 1519, the combined force had reached the Aztec village of Choula. Within several days, the Spaniards (helped by the Tlaxcalans) slaughtered over 3000 citizens of Choula.
At this point, the Aztec emperor Moctezuma II was troubled by the reports concerning about the invaders. A very religious man, Moctezuma beileved that Cortez was actually the Aztec god Quetzacoatl. Luckily for Cortez, his arrival coincided with the year that a prophecy regarding Quetzacoatl was supposed to come true. For this reason, and because of Cortez' white skin, Moctezuma decided to "play it safe" and thus assumed that Cortez was in fact Quetzacoatl.
Thus, when Cortez arrived at Tenochtitlan on November 8, 1519, Moctezuma greeted him warmly and even kissed his hand. By this point, Cortez had a translator, a woman named Malinche (sometimes called Dona Marina). She had joined the war party and Malinche made possible communication between Cortez and Moctezuma. After that initial meeting, Moctezuma allowed the Spaniards to enter and establish a headquarters in a large unused building. Since Cortez' behavior was somewhat less regal than that which would be expected of a deity, Moctezuma began to have suspicions of his divinity. Hoping that a sizeable gift would make the Spaniards go away, he presented Cortez with gold and jewels. Unfortunately for Moctezuma, his gift had the reverse effect. Not only did the gift fail to achieve its intended purpose, but it served to incite the Spaniards' greed. Cortez seized Moctezuma as a hostage, hoping for a twofold effect: to gain wealth from a large ransom, and to forestall an Aztec attack.
While Cortez was exploring and conquering the Aztecs, his past actions began to catch up with him. Governor Velásquez of Cuba, not at all pleased that Cortez disobeyed orders and had departed, comissioned a force to find Cortez and arrest him. Sometime around April 1520, Cortez was informed that the arresting party had landed in Mexico. Realizing that he would be found sooner or later, he gathered his forces and set out to meet the expedition. He left no more than 200 men in Tenochtitlan, and appointed Pedro de Alvarado to lead them in his absence. Cortez's struggle with the arresting party was brief: his forces entered the expedition's camp at night and captured the leader. After that, most of the remaining party members were quite willing to join Cortez, their decision swayed by tales of gold mountains that they had heard on Cuba.
When Cortez returned to Tenochtitlan, he walked right into a revolt. In Cortez's absence, Pedro de Alvarado, the man Cortez had left behind to keep order, treated the Aztecs very cruelly. The boiling point was reached when de Alvarado massacred hundreds of Aztecs at a religious ceremony, because he was afraid a revolt might ensue. Apparently, it was de Alvarado's actions that caused the revolt to start. When Cortez arrived, he was allowed to enter the city and join de Alvarado in the headquarters. However, almost immediately after their arrival, the Spaniards (and several thousand Tlaxcalans) were surrounded and attacked by the revolted Aztecs. His force badly outnumbered, Cortez asked Moctezuma to speak to the Aztecs and calm them. The result of this, however, was quite the opposite. Enraged Aztecs considered Moctezuma a traitor, and stoned him when he appeared to speak. Moctezuma died within a matter of days. He was succeeded by Cuitlahuac, who died of disease several months into his reign. The last Aztec emperor, Cuauhtemoc, succeeded Cuitlahuac.
A bewildered Cortez realized that his only viable option was to retreat from the city. On June 30, 1520 (called Noche Triste--"sad night"--by the Spanish) Cortez ordered a full and immediate retreat. Chased by Aztec warriors, the Spanish lost more than half of their men, and all of their cannons. The remains of the army settled down in Tlaxcala to regroup. It took Cortez almost a year, but he built up his forces once again and conquered every part of the Aztec empire--except Tenochtitlan. Finally, in May 1521, Cortez was ready for the final assault on the Aztec capital. The Spanish attacked the besieged city almost daily, and the end came on August 13. When it was all over, over 40,000 Aztecs lay dead, killed by weapons and disease, and the once-mighty Aztec Empire lay in ruins.