There's a few different ways to play FFH MP.
The most common way (at least at Realms Beyond) are Play By Email (PBEM) games. Pretty simple to set up, a player or a volunteer map maker chooses the game settings, and then generates the first save. The turn cycles through players in order from first to last team, with each player loading the save file (like you'd load a saved SP game), playing their turn, ending turn, and then manually emailing the automatically generated save file to whoever is next in the play order.
You can also play FFH games using Pitboss, where the game is hosted on a private server and players are free to log in and out of the game as they see fit. Turns can be timed, so that players have a limited amount of time to play before the turn automatically ends and rolls over. Pitboss can be either sequential, where players go one after another like a PBEM (but join the server instead of loading a save received via email), or simultaneous, where all players are free to log in at any time. Pitboss does not work with regular FFH, but EitB and I think some other mods make it viable.
Finally, you can use Gamespy to host sequential or simultaneous games. The service is unreliable however, and often some players will be able to join the game while for others it won't even appear in the lobby. Summoning Hyborem or Basium or playing with AI also has been known to kill games through Out of Sync errors.