You can talk to other users in global chat, region chat or send them a private message. To talk to other users in global chat click on the chat window at the bottom of your screen and type a message. Once done press the Enter key or the Send button.
To talk to another user privately, click on that users' avatar, and then click on 'More' on the right hand side of the screen. This will open their profile. Once their profile is open, click on the 'Chat' button to chat them privately.
You can also talk to other people in the same region as you by clicking into the region chat. The region chat will be have the name of the region, such as Welcome Center, so you can see which chat is regional.