If they thought they were in India or Indonesia, would they have tried speaking languages from those areas? and in the end, how did the different languages compare in structure and words? And how did they cope with having to learn to speak many different regional languages like the Muscogee or Hitchiti?
My knowledge relates to whalers, sealers and explorers of the Southern hemisphere, particularly in Oceania.
One technique was merely capture - someone from a certain tribe would be simply abducted and kept on board ship or on land to learn from (and to learn) languages. Later they could be used as a translator. This happened in early colonies such as New South Wales to learn indigenous languages, customs and to open up lines of communication.
The other technique - which somewhat overlapped with the first (but not always) - was known as a "walking dictionary". Sealers in particular would take a local "wife", and languages were learnt that way.
I don't have my sources at hand, but you might want to read accounts of Captain Cook's exploration of the South Pacific, and Captain Phillip's establishment of Sydney in the late eighteenth century.
There is always room for discussion, but perhaps the section How did colonialists talk with indigenous people? in our FAQ will answer your inquiery.