I've read many history books about European interactions with Asian kings. But I've always wanted to know how the English, French, Spanish etc communicated with the local kings, especially when they've just landed in a new location, for the first time.
Well, first off da Gama arrived in 1498, not 1492.
Second, the answer to your question is that he came prepared: the expedition included several interpreters who were fluent in various Bantu languages and in Arabic. Remember, the Portuguese had been trading with West Africa for over 50 years at that point -- the first Portuguese traders arrived in what's now Senegal in the early 1440s. And the Portuguese had been dealing with Arabs pretty much forever. Portugal held the cities of Ceuta and Tangier on the northern coast of what's now Morocco, and they did a lot of trading with what are now Morocco, Algeria and Tunisia.
Arabic was a very common trade language all across North Africa, the Middle East and South Asia -- all the way to Malaysia, really. Everywhere there was Islam, you'd find Arabic speakers, because you can only properly read the Koran in Arabic. And everywhere there were Arab traders, you'd find Arabic speakers -- and Arabs traded all across the Indian Ocean.
So the short answer is, da Gama came prepared with translators who spoke fluent Arabic. Going forward, the Portuguese quickly began studying Malayalam (the local language), including by kidnapping some locals.