This is dealt with in the FAQ: https://www.reddit.com/r/AskHistorians/wiki/language#wiki_cross-cultural_communication_and_lingua_francas

Most in depth specifically to your question by /u/anthropology_nerd here: https://www.reddit.com/r/badhistory/comments/2ryuks/myths_of_conquest_part_four_miscommunication/

Generally speaking on European to Native American communication - Columbus did have a translator by the name of Luis de Torres. The problem was, despite knowing several languages including those anticipated to be used by traders in the targeted Indies, none of those languages were used in what became the West Indies. After realizing there was no translator, they kidnapped males from San Salvador to send back to Spain and act as translators. One was renamed Diego Colón (the same name as Christopher's son) and he was later used in other islands as a translator. This same type of thing happened in North America in the 1500s, possibly the most famous example being Manteo and Wanchese returning to London in 1584 to allow the study of their language by Sir Walter Raleigh who was establishing a colony in his newly chartered land he had named "Virginia." Sometimes it was a voluntary curiousity, sometimes it was a forced abduction. Tisquantum had been captured by an English captain, sold in Spain, escaped to England, and returned to Massachusetts only to find his village decimated from diasese. He learned the English language decently well in this adventure and as such was able to translate at the request of Samoset for the treaty between the Pilgrams and Wamponoag.

Trade further broke language barriers as was evident in New England. When Samoset walked into Plymouth Plantation March 16, 1621 he spoke broken English to the Pilgrams. He had learned it from fur trading with European traders settling/trading in New England. Physical gestures would typically be used heavily in this type of communication and language sharing.