Firstly, every royal court had ambassadors from a number of other countries. They didn't live in embassies, as they do today. They were part of the extended royal household.

Part of their job was to frequently send back details of all the events, gossip, rumors, and goings-on in the country where they were stationed. They would normally spend most of their days chatting with people of all ranks, and writing to their own government a few times a week, at least. They normally also had plenty of paid informers, such as servants in the households of important people, who would give them details of what was being said in private.

Once this news got back to the home country, it might or might not be disseminated publicly.

Secondly, and more importantly for the general public, merchants and traders were constantly coming and going between countries and would carry all the news and gossip back and forth.

It was hard to keep secrets in societies where every household had servants, and everyone at all levels of society thrived on gossip.