During execution of the turn your brigades will automatically shoot at the enemy. You don’t have to order your brigades to do this (after all, your men would normally shoot at the enemy if they could).

Artillery batteries will also shoot at the enemy. However, they do not do this automatically and have to be on "fire" or "fire at will" orders.

In this picture, the Union brigades automatically shoot at the Confederate brigade (highlighted in red). The artillery batteries were either given "fire" orders for this specific target, or where on "fire at will" orders, and decided that this brigade was the best target.

All Brigades will fire if they have a valid target in their “fire zone” and in range. As your and your enemy’s Brigades loose strength points, their morale will decrease, making it harder for them to follow orders, and more likely they will not fight as well.

Eventually, if they loose enough strength points, they will run away completely.