Here's a revisionist take on your question: One of the great misconceptions of the conquistador role is that they were in charge of the war. They weren't. The war that shook up the Valley of Mexico 500 years ago was mostly a conflict fought by Mesoamericans using Mesoamerican rules for warfare, most of which happened completely outside of Spanish purview and therefore they did not see or understand what was happening. Cortés managed to work out a system of communication through translators, but he largely did not "get" the allies, rather they came to him in order to manipulate the conquistadors and improve their position against rivals. This fortuitously resulted in the formation of a new Grand Central Mexican Alliance headed by Tetzcoco and Tlaxcala, who are the ones who actually won the war with Tenochtitlan. Later Cortés manufactured a narrative of a Spanish "conquest" to glorify himself and to justify his illegal actions, which he did by making it seem like he was a shrewd chess master pulling all the indigenous strings in order to bring the Spanish king new vassals, riches, and save the souls of the indigenous people.
This revisionist view is part of a new strong line of historiography that emphasizes "indigenous conquistadors." Historians have long pointed out that indigenous people were involved in the wars, but they often cast them as mere "auxiliaries." In the last 30 or so years, the central importance of indigenous people to these wars has become more clear. Describing these soldiers as "indigenous conquistadors" fits better with what they did on the battlefield because it was ultimately they who did the allying and conquering. They decided the routes to take, where the battles were to be fought, why the battles were fought, and recruited other allies to join them (not the Spaniards). They were the ones who did the negotiating, usually out of site of the Spaniards. Generally, indigenous lords appeased the Spaniards with a bit of food and gifts (a great deal at bargain basement prices!), then funneled the violent foreigners straight towards their enemies. Though Cortés was able to communicate in a piecemeal fashion through all this, it's laughable to think that he understood the complex cultural and political world that he entered. Indigenous lords redirected this violent force toward others to deal with, joining him in order to improve their own position vis-a-vis another altepetl (the term that describes how Nahua communities were organized).
The groups who became the Spaniards' allies switched sides when the Spaniards did not abide by the Mesoamerican rules of war. The conquistadors did not retreat when they were defeated, they did stop their wars at the beginning of farming season, or they did not follow the rules of not perpetrating violence on women and children. The leaders cut their losses by switching sides and agreeing to take their new allies onward toward their next enemy. In doing so, they also usually extracted some sort of conciliatory show of alliance formation (as was expected by diplomatic exchanges in Mesoamerica), like a tribute exchange or attack on another enemy town. These actions were not surrenders; the indigenous armies could have kept fighting, but rather they chose other normal diplomatic and military strategies used throughout Mesoamerica. During battles, Cortés was not coordinating much of anything. He hardly had control of the Spanish captains, let alone the tens of thousands of indigenous soldiers around them doing most of the fighting. Conquistadors complained that the Mesoamerican soldiers did not follow their orders. Why would they? They didn't speak their language, didn't fight wars in the same way, and local soldiers had different objectives in mind than did the Spaniards.
Take Tetzcoco as a good example. One of the three cities of the Aztec Triple Alliance, a dynastic dispute occurred in 1516, just a few years before the Spaniards arrived. Cacama and Ixtlilxochitl and others had claims to the thrown and vied for control, with Cacama gaining the support of Montezuma and becoming tlatoani. Ixtlilxochitl and his faction later threw their lot in with the Tlaxcalan army. Together, they retook Tetzcoco and continued on to eliminate remaining Mexica strongholds on that side of the lake. With each victory the Tlaxcala/Tetzcoco army cemented their power and gained access to more soldiers, plunder, and prestige. I'm summarizing here heavily, but you can see that the conquistadors had little to do with this struggle and did very little, if any, coordinating, only later writing that they had flawlessly planned and executed the whole thing. Yet the war was fought almost entirely by indigenous people, for indigenous objectives, which were rooted in a long Central Mexican history.
So although translators proved important in the short term, there is also more to the story than simple conversations with disaffected Aztec tributaries. Deeper historical rivalries and war strategies provide an even more satisfying answer.
For further reading, I recommend Matthew Restall's Seven Myths of the Spanish Conquest and When Montezuma Met Cortés. Camilla Townsend's new book Fifth Sun is wonderful. She also has a really good book about Malintzin called Malintzin's Choices, which focuses more on the woman who translated for Cortés. On indigenous warfare, anything by Ross Hassig. There is a recent book on Tetzcoco, one called the Lords of Tetzcoco by Bradley Benton and another called Texcoco: Prehispanic and Colonial Perspectives. There is also a recent translation of Alva Ixtlilxochitl´s account called The Native Conquistador: Alva Ixtlilxochitl’s Account of the Conquest of New Spain. For more on indigenous conquistadors in general, see the book Indian Conquistadors, edited by Michel Oudijk and Laura Matthew.