If you are online and logged in to your booth on Biblio.live and have not opted out of chat, then customers will see the option near the top of the booth to open a chat window with you:

When a customer sends you a chat message.  You will see a chat request in the bottom right-hand corner of the Biblio.live site:


The red circle shows the number of unread messages.  When you see that, click it to open the chat window.
The 'hamburger' icon (three stacked horizontal lines) at the top left of the chat window will show a list of the users you have chatted with.  That is circled in red here:

From the user list you can click any of the other users to resume chatting with them.