1. On the blue navigation side-bar, you'll see a "Direct Messages" section. this is where all your current direct messages (even those from other teams) will be displayed. To send your first direct message, select the "more..." link under the section header. Then, select the user you want to message from the modal. 

This will begin a direct message chain. You'll be able to tell from the side-bar whether the user is online, away, or offline entirely. Furthermore, a teammate's name will be highlighted if there are new messages for you to read.