Even if you aren't playing a game with them, you can still live chat with your friends!
To open a chat window, hover over Connect in the left menu and click on the Chat tab. You'll see a list of your active chats. Click on a friend to open a chat window and continue your conversation! If you haven't chatted in a while, the chat will move to Inactive Chats. Click there to see all your old chats
If you haven't chatted with your friend yet, click on the Friends tab and hover over their name. Click on the 
icon that appears to open a chat window with them.
You can click on the 
icon in the lower right to see all the different emojis you can add. To close the emoji window, press the Escape key or the X at the top right corner of the window
Then, just type your message! The chat window will stay open on your screen, even if you're navigating other areas of Chess.com or in a game. Click _ to minimize the window or X to close it, but your messages will still be there when you open it again.