This of course really depends on what time you are talking about, but I guess that up to the invention of motorized vehicles and the telegraph/telephone, most communication went through messengers. Each country/area had different methods for this, but for long distances I think there were two major ways: either by horse when over land, or by ship over the water.

I do not know much about messages that went by ship, so I will leave that for others to verify.

However, I know that at least under Augustus (and probably during much of the Roman Republic/Empire), there existed a sort of relay system, where a message would travel from post to post, until it reached the destination and could then be delivered to the intended person or at least city. This would always be done by horse, since this was definitely the fastest, although some areas were, as already alluded to, easier to reach by ship.