There is no post office as of yet. To send letters to be received on other characters mailbox posts, here's how they work in game.
Simply write whatever you wish to sent on a piece of paper or what have you as well as the number of the house of the person you want to send it to. Place it in your mailbox, close the lid. It will immediately be sent to the appropriately numbered house.
One can also place fitting items in the mailbox and have them sent, as long as the house number is written on them or fastened to them in some form or fashion. This can range from gifts to the carefully crafted pipe bomb, so be careful! When a character receives mail in their box, their mailbox flag will go up so that they know they have received mail.
When you send someone a letter (i.e. comment on their mailbox post) it is assumed their reply is being sent back to you, even though the thread will continue on on their post. It basically just tells who initiated the mail and then so on and so forth.