Answer:
Reading some of the explorers' diaries of that era makes it clear that communicating with new peoples was a known issue, and that there were fairly clear and well-defined toolboxes to deal with it. I'm thinking particularly of Joseph Banks' Endeavor voyage notebooks, but I've seen the same thing in others. They meet a new group of people with a strange language, and rather than freaking out over it they matter-of-factly begin to collect nouns and verbs, and pick up a working vocabulary in an impressively short time. It was part of the expectations, really.
It's likely that this attitude and approach didn't carry over to the actual colonists, as opposed to the explorers, but at least they could take advantage of the initial work if so desired.