From my understanding of history, the Spanish were able to team up with many Native tribes in order to overthrow their oppressors, but without any knowledge of Native Languages, how did they manage to convince the other tribes to join them against the triple alliance? To be more precise, how were the Spaniards able to learn those languages so quickly? This also applies to how different languages were able to be translated into other languages.
Hi to start I would reccomend a book called malintzins choices by Camila Townsend if you want to better understand the story of the interpreter who helped the Spanish translate with the Aztecs and their enemies. To answer your question though its important to realize how long a process the conquest of Mexico was Columbus first discovered america in 1492 and Cortez would not start his invasion until 1519 in that almost 40 year time frame Spain had already conquered the west indies and had set up some semi permanent cities (alot of them were destroyed by natives many times). During this time individuals would learn the local languages. Notably one individual who would prove valuable to Cortez is a Friar named Geronimo de Aguilar who after being a slave for 8 years to a mayan chief would learn yucatan maya the language of the coastal people of that area. However the Moctezuma the leader of the Aztec triple alliance did not speak yucatan but a language called nahuatl. Cortez would get ahold of a slave girl named Malintzin who spoke nahuatl and yucatan when he was gifted 20 slaves by the lord of Potonchan. By having malintzin translate to geronimo and geronimo to cortez they were able to communicate with the enemies of the Aztecs. Eventually Malintzin would learn Spanish and become cortezs primary translator, she would even later birth his first son. Hope my answer was helpful.