Messages are sent both from the daemon and from other players. They appear in the message window at the bottom, right side of the display. To send messages, just put the mouse into the message window. You must type a character in that represents the recipient of your message. This can be 'A' for everyone, the first letter of a team name to send to all members of a given team, or [0-9abcdef] will send a message to an individual player. When you've typed this in, it will map to a proper address and wait for you to type in some text. When you type in a return, your message is sent. Typing an escape will abort the message in progress.
This is obviously a non-optimal addressing mode (for instance, a team 'Acturians' screws things up), but it is the best we can think of, and also the original.
Now obviously, the next question is, "What if someone starts shooting at me while I'm typing in my message? Am I hosed?" Simply move the mouse out of the window to defend yourself. Messages are only dealt with if the mouse is in the window. You can stop in the middle of the input.