Make use of room variables to keep track of which players have arrived.
Using the sendMove() method of the ElectroServerAS object, you can very easily send information to your opponent.
The sendMove() method allows you to send objects. It is a good idea to use a property on the object, such as type, to concisely describe why the object is being sent. For instance, in checkers you might have a special move for making a checker a king. In this case, the type property would be "king". For other moves it would probably just be "move".
Don't forget to use the joinGame() method when you have reached the frame that displays the game; otherwise you'll be playing a game in a regular chat room!
Turn-based games are easier to build in Flash than real-time games; however, real-time games are possible.