Or you could just check your system maps of the nearby star systems to see if only one faction is at war, which may indicate its at war with the faction in your current system. I haven't participated in a multi-system war, so I'm not really sure of a better way to find out who is at war.
Just in case you experience this uncommon bug- if you enter a conflict zone and only one faction is available to choose, then leave the conflict zone immediately! You may have to restart the game to straighten things out if this is the case.
But you do have to look for conflict zones to find them.... Just curious, is the war in a system that has another star far away from the first star you jump to? If so, the conflict zones might be there.