Rule of thumb: ancient peoples were no more stupid or ignorant than we are, they just had less technology.

In 1519 in Mexico, the young Malinche was given as a slave to the conquistador Hernan Cortes. Until then she had lived as a slave with the Maya, having spent her childhood as part of the Aztec aristocracy. She was therefore bilingual, speaking both Yucatec, one of the Maya languages, and Nāhuatl, the language of the Aztec empire. The conquistadors soon realised her linguistic abilities and she became a key interpreter during the Spanish conquest of Mexico. Before long Malinche was also able to speak Castilian, but at first she translated from Nāhuatl to Yucatec and vice versa, while Gerónimo de Aguilar, a Spanish friar who had spent eight years among the Maya, translated between Yucatec and Castilian.

As you see, even between cultures separated by millennia and whose first contact was less than 30 years earlier, you found people capable of learning each other's language. Finding interpreters was even easier when the two cultures were territorially close and had had diplomatic and commercial exchanges for many centuries. For diplomats, then as now, knowledge of many languages was essential to their work. In lands outside the usual range of diplomacy, a good alternative could be merchants.

As for your question whether ancient languages were similar, this is no more true than for today's languages. Territorially close languages could have a common ancestor and thus be quite intelligible with each other, but they could have completely different roots and thus be unintelligible.