How did mail service worked in ancient times?

More precisely, how did it work (and how complicate it was) to send a letter far away, for example in a different state?

The specific reason why I was thinking about this is the Bible, in particular New Testament, which contains Letters of several apostles (mostly Paul, in the Catholic Bible there is also a bunch of letters of other people, such as James, Peter, John, etc...), however after I thought about it, I become curious about mailing service in general in ancient times (but feel free to limit your answer to only the Roman Empire and/or other historical periods if this become too broad of a subject...)

I'm not really concerned about the authenticity of those documents, I was more curios on whether or not it would be possible, and how accessible it was. In this particular example we are in the Roman empire, however those letters are sent in very different (and far away) provinces (Greece, Turkey, etc...).

Regarding the Roman Empire:

1)How expensive it was? Was it possible because Paul was a Roman citizen (and, I guess, relatively rich)? Or maybe it was funded by the money collected by the Christian communities?

2. How would they be able to sent the letter? Was there some sort of state-managed postal service (maybe through the army?) or would they have to find a private courier?

3. Was there any reason for ordinary people (i.e. no nobles, no rich merchants) to sent letters? Would they be able to read? (I know writing was more complicated, but what fraction of the population was able to read?) For example, maybe soldiers who were stationed in some place very far away? Would they write to their families?

More in general, how did those things changed in the Middle Ages? Was it still possible to send letters? Was it limited only to within a certain state, or was it possible to send it in other regions as well?