Go to My Home---->Messages
http://www.chess.com/home/messages.html
Click on 'Compose New Message'.
Enter in their username, subject, and your desired message.
Ask them to send you a challenge game or they can change their options to allow challenges.
How do I send a message to someone who is not on line and who has no game pending with me? When I tried to start a rematch, as we planned in the previous game, I got an automated reply that she is not accepting challenges.