Back in our early civilizations, how did people from different empire/country interact with each other without knowing a common languages before hand?

They found someone who did or managed with sign language or such until such an individual could be found.

Several folk have a knack for languages, and given the nature of Human migrations, it's usually not difficult to find a population with a lesser degree of linguistic drift from one's own compared to that between the original two tongues in question. In case of completely different populations- such as the pre-Columbian Americans and Spanish, it might be a tad more difficult but nothing time and curiosity can't fix.

This is also where Scholarly Tongues and Trade Pidgins played a major factor. Until the 19th Century, ALL educated Hindus had to know Sanskrit without exception, and as a result even regional tongues had so many Sanskrit loanwords that the average 19th Century Hindu would've been a defacto unperson in our great modern colleges.