You can watch a match in progress by selecting one of the player's name in the Lobby, and watching them (using the Action > Watch menu command, or clicking the Watch toolbar button).
When you begin watching, the Board window will open automatically, and the Lobby window will zoom down to the Toolbar (this behavior is configurable in the Preferences window.) The player you chose to watch will be the bottom player.
Note that you cannot watch one of the GridGammon robot players, since each robot plays multiple games. You can watch a player who is playing a robot opponent, however.
You also cannot watch a match that has been marked Private.
To stop watching a match, just close the Board window! Use the File > Close (Cmd-W) menu command, or click the red button in the title bar.
To play a match you must first initiate or accept an invitation with another player. To indicate you are available to play, mark yourself Ready (using the GridGammon > Ready menu command, or clicking the Ready toolbar button in the Lobby window).
The Board window will open automatically when you and your opponent have agreed to a match, and the Lobby window will zoom down to the Toolbar (this behavior is configurable in the Preferences window.)
Basic information about the Board window
How to move roll, move checkers, etc.
If you have finished your match, you can stick around and chat with your opponent or any watchers. When you're ready to return to the Lobby, just close the Board window to leave the match.
If your opponent leaves (and there are no watchers), the Board window will close automatically, returning you to the Lobby.
If you close the Board window before you have finished a match, the software will ask whether you are sure you want to leave. If you do, your unfinished match will be saved, and can be resumed later.