To play a game, you must initiate or receive a match invitation.
To initiate an invitation, select the player in the Lobby window and click the "Invite" toolbar button (you can also use the Invite menu command under the Action menu). You may have multiple invitation windows open, but the first one accepted by you and the opponent closes all the others.
An invitation specifies the match options, including the variant (backgammon, nackgammon, or hypergammon), the match length, whether the match will be rated or unrated, and doubling cube options. If both players have cash accounts, the invitation also may be used to establish a wager on the match.
Invitations are negotiable. For example, you may receive an invitation to play a 7 point match. If you don't feel you have enough time, you can modify the invitation to indicate you'd prefer to play a 3 point match instead. If the player who sent the invitation agrees to your change, you can then start the 3 point match.
You may instead decide the match conditions are unacceptable, and close the invitation dialog to decline the invitation. You can also chat directly with the other player to discuss the invitation.