First off, Saint Paul never knew Jesus. This is a very common misconception. He was not one of the original 12 apostles. He was a Jewish/Roman military man of the Roman Empire who at first persecuted Christians, then later converted, became a missionary and became arguably the key founder of Christianity. He was from Tarsus, Cilicia. He lived from 5-67 a.d.

Anyway, I'll try to answer the question as best I can, I'm no expert.

The Roman's postal system was incredibly sophisticated and advanced for the time period. It was very simple for one to send a letter almost anywhere in the empire as long as it had an address. Paul's letters were often addressed to cities he or other missionaries had started Christian followings in. Often they were written to answer theological questions that arose in these congregations from a lack of a central or canon Christian law. The beginning of Christianity saw much debate and disagreement with different interpretations of the different gospels and the reality/divinity of Jesus. The letters would often be sent from Paul to the known Christian leaders of specific towns. These letters were to be read aloud to the following of Christians during their time of worship and congregation together. During the infancy of the Church it was common for letters to be sent out, there were always questions that needed to be clarified by one who they believed had an authority on the matter.

So I'm going to begin with one caveat. What I know about is the 4th century letter networks primarily amongst bishops, not the high imperial postal system of the 1st-2nd century of Paul's world. So bear that in mind.

Letters outside of official government communication were not delivered by the imperial post (i.e. post office), they were delivered individually, by slaves, friends, or trusted individuals who would be chancing by the recipients location at personal cost to the sender or the messenger.

I don't precisely know what the mediums were, but I presume a wax tabula or a scroll. Tabulas tended to more durable, but considering the length of some of these letters, I can't imagine papyrus scrolls not being used for communique.

There was a low expectation of privacy amongst late antique letters (doubly so outside of secret government communication) and many were written with the intent for them to be published.

This is "non-presumption of privacy" is an important thing to consider, as this is why late antique letters don't read like modern ones. Modern letters are considered intensely personal, not meant for dissemination, and usually a chronicle of autobiography or recent history. Ancient letters straddle what would be considered many modern genres. They could be philosophical treatises, essays, political commentary, panegyric-like praises, educational recommendations, in addition to autobiography and history. They were intended to be "instructive" as well as "informative." This is why, regardless of whether an author cared for a letter to be saved, letters would be recirculated and sometimes published. At the very least, most letters (at least those that were saved) were not intended to be fully private.

To whom were the letters sent? To whomever they wanted. There are plenty of records of soldiers on the frontiers sending letters back to their family at home. However keep in mind, that outside the military, the only people who had the need to send a letter, were usually people who had the means or could afford to not be forced to live as part of the agrarian 80% of the roman world, tied to their lands by basic necessity or law, i.e. merchants, bishops, officials, senators, etc.

When letters were received, they could be read alone or in a large group, but often the letter bearer was thought of as a stand-in for the person delivering the letter, so he would sometimes be invited in as a guest and quizzed about whatever details and circumstances regarding the letter and the letter sender. This would naturally result in the letter being re-read to the close ones of the recipient as well.

Off the top of my head, I don't have a late antique example of multiple copies being made, but considering the known unreliability of letter transportation, for important communication this must've been so. I know as an example from way later, from the 16th century, Matteo Ricci would send multiple copies of his letters from China back to Rome via dual ships traveling in different directions. One east via the Americas, one west via the Indian ocean. In the Late Antique world, it was considered the responsibility of the letter sender to maintain regular contact, which was frequently revealed in the introductory rhetoric of most letters, lamenting delays or praising prompt replies, so if multiple letters weren't sent, I presume a summary would be attached in the next one if one was lost.

Some sources I'm pulling from:

• Ebbeler, Jennifer. “Tradition, Innovation, and Epistolary Mores.” In A Companion to Late Antiquity, edited by Philip Rousseau and Jutta Raithel, 270–84. Blackwell Companions to the Ancient World. Chichester, U.K. ; Malden, MA: Wiley-Blackwell, 2009.

• Gibson, Roy K. “On the Nature of Ancient Letter Collections.” Journal of Roman Studies 102 (November 2012): 56–78. doi:10.1017/S0075435812000019.

• Sotinel, Claire. “How Were Bishops Informed? Information Transmission across the Adriatic Sea in Late Antiquity.” In Travel, Communication and Geography in Late Antiquity: Sacred and Profane, edited by Linda Ellis and Frank L. Kidner. Aldershot, Hants, England ; Burlington, VT: Ashgate Pub Ltd, 2004.

• Walsh, P. G. 35. Letters of St. Paulinus of Nola, Vol. 1. Westminster, Md.: Paulist Press, 1966.

You already received a comment about the postal system so I wanted to point out that he actually states in a few of the letters who was delivering them. I just got to work and can't put a lot of time into this, but the two examples I was able to quickly find are Phoebe who was sent to Rome (Romans 16:1) and Timothy in Thessalonica (1 Thessalonians 3:2).

Paul states that these two were sent as leaders of the church to help that particular congregation. It is possible that they followed the letters or preceded them, but the general consensus in my studies was they brought the letters themselves (they were going anyways) and would read and instruct through them to make sure the message was understood.