It is usually assumed that the relevant date for the landing in Mexico of the Spanish, and the begin of the conquest was February 1521 (although in there was campaign in 1517 to Yucatan, at the time inhabited by the Mayas, a different culture and today Yucatan is within the borders of Mexico. Furthermore, first accounts of Spanish contact with Yucatan go back to 1511).
At the time the Aztec leader was Moctezuma II. (until 1520)
Further, during the conquest there were other leaders:
Cuitláhuac (1520) Cuauhtémoc - in 1520-21.