How do you play Heroes of Might and Magic 3 online with multi players?

Guessing here...

Make sure the correct ports are open in the router of the player acting as the host, have that player set up a multiplayer game, then have the other players connect to the host's IP address.

Alternatively, there are applications that let you set up a VPN -one example is Tunngle- and play as if you were on the same network, should make it easier if the game automatically finds game hosts on the same network (but I don't remember if HoMM3 does that).