So I adapted our test game:
It is a HotSeat game now, everybody has the mapmaking to be able to exchange maps, 2 other techs, money and four new warriors (2 of them close to cities of opponents). The diplomacy can start.
I suppose we will do the contact by e-mail (?)
Since there may be some events (for example new tech, famine...) at beginning of the turns, we must save the game at ends of turns. So my instructions for a hotseat game were wrong and I have to change them:
Start the civ2.exe, load any (singleplayer) game and drag the Civ2 window down, so that you see just the blue system bar (I have a text "Civilization II Multiplayer Gold" on it) and so you don't see the map, press Ctrl-Q, say Yes: You are in the main menu.
Choose Multiplayer game/Hotseat etc. You get the message like "Lenin, you may now command the Greeks", where Lenin is your predecessor. Press Enter to close the message, press Enter again to finish the turn of your predecessor. Then play your turn, press Ctrl-N if needed (if some activated unit is left), save the game, press Ctrl-H (it replaces the Ctrl-Q hotkey in hotseat mode) to finish the game.