Because the order of movement and firing on the battlefield is based on initiative, regiments must act or not act when they get the chance.  Often it is useful to avoid firing on your turn, preserving that regiment's fire for opportunity fire during an opponent's move. 

When one of your regiments is selected you fire by placing the cursor over an enemy in range and clicking. You see the cursor change to a crosshairs if the target is in range, and to a red X over a crosshairs if out of range.

You move an active regiment by clicking on a green or red pip on the battlefield. Because the enemy can fire during your move there is no way to take a move back. However, you can move in multiple steps clicking each time a little bit nearer to the enemy. There is no reason that an active unit has to move its entire distance all at once.

An active cavalry regiment stays active until you click on the unit itself to end its turn or until it has fired its weapons and used its entire movement. Infantry and Light Artillery cannot move after firing, but can move and then fire. Heavy Artillery cannot both move and fire in the same turn, but light artillery can.