Only Washington D.C., Paris, or Moscow count as city maps. To play on one of those, either your faction has to attack a city or see your capital be attacked by an enemy faction. This is nothing frequent (usually) and will only occur for a small amount of time during a war, usually at the end.
City battles consist of three rounds. You can play during any of those and it will count. You do not have to win. This can only be done online in the Theater of War mode.