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.
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.