Hollywood always seems to have the Magical Universal Translation of Oxford accented English for every ancient ruler of every country throughout the whole of human history. However, I'd assume with some of the massive spread of real estate guys like Alexander the Great or Genghis Khan had, they must have run into people who didn't speak the Mother Tongue. Did they carry around professional translators as they rampaged and conquered neighboring civilizations? Did diplomacy or assimilation ever fall apart because of difficulty communicating?
There were the Koine or near-universal tongues for nearly every region. Think of English in today's business world. ASEAN's Singaporean president said in 2004, after a meeting was held by nearly every Asian country -- entirely in English, without the US or Brits being there -- "I commend to you the virtues of the English language." In the time of Alexander, it was Greek (for the Mediterranean and surrounding areas). Even Pythagoras, in Italy, and Archimedes, in Sicily, and Ptolemy, in Egypt, thought, spoke and wrote mostly in Greek. It was Aramaic in the Near East, and Persian in the Middle East. There was a precursor to Hindi/Urdu/Punjabi in the region of India. Genghis Khan had Chinese and Persian employees, and you're right, he had to capture or employ translators for smaller languages into one of these Koine, from time to time.
So I am not a historian, I am just a Classics major. However, I can tell you about two Greek authors (Xenophon and Herodotus) who discuss this. The Greek word used for this is hermēneus (ερμηνεύς). These were people who were bilingual and were kept in the court of royalty or in battle along with generals.
Herodotus uses a translator as a guide in Egypt and Persia. Herodotus is a man traveling all around the ancient world making inquiries to learn about events. It is never specified where Herodotus obtained his translators, but they are interesting nonetheless.
Xenophon was an Athenian mercenary general in the army of the Persian Cyrus the Younger. His Anabasis has many details on translators, but no large specific chapter pertaining to them.
Unfortunately I cannot go into more details, I have to continue studying for this Lyric Poetry final. Good luck!