In order to start a multiplayer game, both players must agree upon who will be the Host, and who will be the Client. The Client will also need to know the Host's IP address.
The Host should select the "Start HOST game" option from the Network subgroup (found in the Start Menu).
The Client should select the "Start CLIENT game" and proceed according to the instructions.
After both games have launched, both players should click "NEW GAME", "MULTI-PLAYER GAME", "DIRECT CONNECT", "CONFIG", "COM 1" and "38,400 BAUD".
Now the Host should click "HOST" and the Client should click "GUEST".
The rest should be straightforward, as far as archaic multiplayer systems go. ;)