It is possible to play the game over a network connection with another computer. To do so both player on both computers have to select one colour played by a human player and the other by the remote player. Who chooses which side does not matter. It even does not matter if both choose to play the same player as this will automatically be interchanged by the game.
One of the computers will act as game server. Only this one can start a new network game. Also all its game data will be transfered to the client computer. You can force your computer to be server if you do not supply a hostname in the network dialog. This dialog pops up if you start a new network game. As a client you enter the hostname of the machine the server is running. The port needs usually not be changed. But you can enter nearly any number there.
When a network connection is build you are ask to enter a remote host and a port. The port can usually just been left untouched. But if you now what you do replace it by another number, which has to be the same in both player games of course. The hostname should be the name of the remote host to which you are connecting. Only one of the two players has to supply a hostname, the other one need not to, but can.