When it comes to the Silk Road, for centuries Europeans could learn to trade with someone in Eurasian region over generations, who could then trade with someone who could trade in the Indian subcontinent, who would trade with someone who could speak enough Chinese to trade in China.
This all changed after people set sail on a global scale. Voyages took months, and one would assume they did not have translators. The Portuguese who had rights to stay at the fringes in Japan probably did not speak English. So how did Commodore Matthew Perry expect that the letter from President Fillmore would be read and understood by the Emperor?
200 years earlier, when it comes to Italian painters like Giovanni Niccolo and Portuguese missionaries around same time period, how did they communicate with the Japanese? Did they just settle near a beach somewhere and just tried to give gifts to locals as a means that they were not invading forces?
Often times, there was some shared language between the cultures, even if it was neither nation’s native language. More can be said if anyone has something more to add—especially regarding trade and communication with East Asia in particular, as that seems to be a more focal point of OP’s question—but the FAQ actually has a whole section on Cross-Cultural Communication and lingua francas. In particular, you might be interested in this answer: