The way that Europeans first communicated with Native Americans upon first contact varied from place to place. However, there were a few methods that many used in order to bridge the language barrier between the two peoples.
This usually started off with simple non-verbal communication. Mimicking actions, using charades, drawings, and demonstrations were common starting points. Christopher Columbus described in his journal showing the Taino a sword to demonstrate the power of metal weapons, for instance. From there they developed a rudimentary form of speaking using simple vocabulary from both their languages.
Other times the Europeans captured native children and taught them Spanish. They then served as interpreters between the two peoples. Fransisco Pizarro did this when he first went to Peru. Once the children learned enough Spanish they would sometimes be returned to their homes in order to serve as a cultural and linguistic bridge. Other times these children were kept as servants by the Europeans who kept them with them on their expeditions as translators.
Other times the Europeans brought a native translator with them. This was the case with Cortez and his indigenous consort known as La Malinche. She learned Spanish rather quickly and her knowledge of local languages and customs helped her serve as an intermediary for the conquistadors and the native peoples of Mexico.
Sometimes Europeans were able to quickly learn the native languages. When Cortes landed on the island of Cozumel on his way to conquer Mexico, he encountered two shipwrecked Spaniards who had learned the Maya language. They were able to help the Spanish communicate with some of the native peoples they later encountered.
On occasion, the colonists were fortunate enough to encounter someone who already knew their language. This was the case with the Pilgrims and the Wampanoag tribe in Massachusetts. A Patuxet known as Squanto had some years earlier been captured and brought to Europe as a slave. He lived for some time in England where he learned English before finding a way to return to his homeland. When the Pilgrims arrived Squanto served as a translator and intermediary between the two peoples.