You can have your hero move with their army whenever you choose. When you perform the Move Hero Action, you will be moving your hero with their army to another adjacent territory. You can move before or after any other Hero Action like Build, Recruit, Publish, or Battle. For instance, if your hero has gained the ability Action 4, that hero has 4 Hero Actions he can perform. So you could conduct an opening move (costs 1 Hero Action), attack an opposing hero’s army twice (costs 2 Hero Actions), and then conduct a closing move (costs 1 Hero Action). Consider another example. If your Confessor hero has 4 Hero Actions, you could perform an initial move (1 Hero Action), Publish a writing in order to try to convert an adjacent territory (costs 1 Hero Action), and then move two more times afterward (2 Hero Actions). With your hero’s army, you may not move through a friendly territory with another hero’s army in it or ever have two of your armies occupy the same territory.
A very important strategy in developing your heroes’ abilities is moving into unclaimed territories. If you move one of your other heroes out of a territory, it has become an unclaimed territory. If you then move another hero into it, this hero can gain a square on the ability chart. This movement is a very crucial part of your strategy. Figure it into your overall plan when you place your heroes and soldier markers at the beginning of the game. This type of movement into unclaimed territories could be considered campaigning for league support! The locals are always impressed when you come to town in person!