The edit window closes
A message can only be edited for a while after it was sent. Once that time has passed, Edit reports that the message can no longer be changed.
Messages are one to one and stay on the site - no group chat, no email round trip. Whether you may write to someone depends on whether the two of you follow each other.
My messages in the menu under your name opens the overview: the people you have exchanged messages with are listed on the left, the selected conversation fills the right. The rule the page states itself is that you can message people you are friends with, or people who accept messages from everyone; for anyone else the page says you cannot message this user.
Find them in the member directory
Members in the top bar, then open the person's page. It carries a Message button beside Follow and Block.
Write and send
The input sits at the bottom of the thread. Send posts the message, and the conversation joins your list from then on.
Fix a typo
Edit on one of your own messages reopens it in place. Save keeps the change and marks the message as edited; Cancel edit leaves it as it was.