It's less than ideal. Basically a player only sees lines of text in chat that are entered AFTER they have entered the chat screen, which you can discern by their flag disappearing at the top of the screen.How can you communicate while playing the game between just two players? The chat screen automatically goes away when both players end their turn so when would you get a chance to discuss anything?
If you need to say something to another player, you basically type out the line of text you want to send in the chat area, but don't hit the enter key until you see their flag disappear. If you hit it just after it disappears, the text will be on the screen for anywhere from 1-5 seconds while the turn is processed, and hopefully, if they are paying attention, they will see it.
This is really the only way to communicate within MOO2 if your empires are not in contact. It's poor at best, but it is sufficient for asking to save the game because you need to stop playing..."Save, pls", for instance, or "Long turn, gotta help kids out".
-Gusset