When another person joins your BlackJack or Roulette table, or when you join a Public Table where someone else is already playing, a "Chat" button will appear at the bottom left of your screen (next to the "help" button). Just click on it and start chatting in the chat box that opens up. To close the chat box, click on the "Chat" button again.
The other players will only see what you write if their chat box is open as well. The chat box will flash to notify you that the other players are writing messages.