Those conversations would have been aided by familiarity with Arabic. It was a language somewhat common both in Portugal and India and all the way in between both as it was the lingua franca of the muslim world. Portuguese sailors could communicate well enough in with Arabic speakers, been doing it for centuries in their homeland and they expanded into the sea they came in contact with even more in Africa. Arabic also propagated in the Indian subcontinent for just as long via trade routes and conquests and Vasco da Gama had knowlege muslims existed in those lands. Either by bringing an arabic speaker as crewmember or recruiting someone fluent in culture of his destination along the way Vasco da Gama could ensure communication with locals at least at a basic level.

There is a story that once Vasco was asked what he wanted the response was "Christians and spices" so at least he presented his intentions clearly since some deals where made and he got half of it. On his second voyage back to India, Vasco return with a war fleet, a universal dialect that did not need translators and began taking over the trade opportunity he had been refused the first time. This marked the start of Portuguese presence in the region and communication and mutual understanding became more accessible.