Check out this article to learn how to chat with a friend: How do I open a chat window with my friend?
Chess.com has a messaging system that works much like email. You can send a message through your inbox, or by clicking on a user's name and selecting the message icon.
Send a new message via a member's profile
You can click on the username of the member you want to message anywhere on the site and click on the
icon from the pop-up menu
You can type a quick message here and click send to have it appear in the user's inbox. For more detailed messages with formatting, images, or other elements, write the message in your inbox. To access your inbox, click the
icon in the upper right corner.
Click Send to deliver your message.
Send a new message from your inbox
If you’ve already exchanged messages with someone, you don’t need to click New Message Just open the existing conversation, type your reply, and send.
Hover over the Chess.com logo and click Messages
Click on New Message in the upper left corner of your inbox
Type into the Search Members box to find the person you want to message
Type your message in the text box - The icons above it allow you to insert a game or diagram, insert an image, add smileys/emojis, bold or italicize, and add or remove hyperlinks.
Type your message and click Send when you're ready to go!
Check out this article to learn how to manage your inbox: How do I manage my inbox?