you can send a message when you make your move. There should be a message link next to the 'move' button. After you have entered in your move, click the message link, type in your message, and after that click the 'move' button.
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The above is for sending a message to your opponent during a game.
In addition, you can send a private message or PM to anyone at any time by clicking on their username. At the top of the profile page there will be an option to send that person a PM. These messages are viewed and managed when you access your 'inbox', which you will find listed on the 'My Home' page.