Types of chat
Channels
Channels are group chats that can be accessible to all users or restricted to specific members. For example, an open #off-topic channel for all users or a restricted #moderating channel for admins and moderators.
A channel with new messages will have a colored dot next to its name:
Personal Chats
Create Personal Chats using the 
icon next to the Personal Chats header. If in Full-Screen Chat, hover over the header to reveal the icon. User cards also allow initiating chats.
Accessing chat
Provided your community has it enabled, you can access chat by clicking the speech bubble icon next to the search tool at the top of the page. Clicking the icon again will close the chat window. Channels with new messages will show a colored dot:
If you have new messages in Personal Chats, the icon will have a green dot.