Just as an example, when the Europeans arrived in America. On initial contact, their cultures would be vastly different and their languages would have little to no common roots. But eventually they got around this, and people from both sides could learn the language of the other. How would they go about setting this up? I have often heard that missionaries were charged with learning the languages of other cultures in order to facilitate conversion, was there ever a standardized system for how to learn a completely foreign language?
Burling, Robbins. Learning a field language. University of Michigan Press, 1984.
The techniques of language learning without benefit of a written grammar are outlined in books on learning language in the field. Several of the colonial diarists mention some of the same techniques, which are using visual cues (including pointing) and learning nouns.
Most humans can enact/demonstrate about 200 words, easily (see above citation). These form a core vocabulary that can then be shared across languages. Many have heard of "Indian sign language," which was a fairly broadly shared system of enacting lexemes so that meaning could be conveyed and language learned across language groups. It makes sense, since there were so many languages in Native America. This comes as close to a standardized system as I know. See also:
Silver, Shirley, and Wick R. Miller. American Indian Languages: Cultural and Social Contexts. University of Arizona Press, 1230 N. Park Ave., Suite 102, Tucson, AZ 85719, 1997. (Good bibliography in this book).
As a follow-up, are there any notable incidents where a mistranslation significantly affected the events that followed? If not between Europeans and Native Americans, say, during one of the major world conquests where the conqueror came upon a people they'd never encountered before (Roman, Arab, Mongol, Chinese)?