There are two ways to send chat messages in BigBlueButton; public and private chat messages.
To send public chat messages:
The Public Chat  controls are located in the in the upper left-hand corner.
If you do not see the public chat option you may need to select the Users List / Chat Toggle  to expand the users list panel and public chat.
When the users list is expanded, the public chat will show a count of any unread messages that have been minimized (in red).
Select Public Chat  to expand the public chat panel. To hide the public chat panel, select the “<”  symbol.
Use the Chat Input  field to type messages into the public chat. Your chat messages (and messages from other users) will appear in chronological order.
You can save or download public chat by selecting Chat Options  menu.
Select either Save  (you will be prompted to download the public chat as a text file), or Copy  (the public chat will be copied to the clipboard).
To send private chat messages:
To private chat with another user, select their name (a pop-up menu will appear) and choose Chat .
A Private Chat panel will appear. To hide the panel, select either “<”  or “x” 
Use the Chat Input  field to type messages into the private chat.
As with the Public Chat, you will see a count of unread messages (highlighted in red) next to the user name.