You've Got Mail!!!

And it's being delivered by our very own postal piggy, Hermes!  If you see Hermes randomly spawn to you, right click him -- he'll give you your letters.

To start writing a letter, open up chat by hitting 't' and type "/letter" followed by your message.  When you're finished with your letter, type "/post (username)".  

Hermes will make his round every 30 minutes.  You can also drop your written letters into chests or hang them on walls with item frames.  

Here's a tutorial video if you need more help: