From observation:
Basically, click the battery activator, it will highlight.
The number represents the number of power units that you can expend on demand (there is a little delay)
If you have perfect energy balance at that point, the power in the battery is not needed so the value will stay constant, as soon as a ships system need power (for anything includeing shield reinforcemt of any kind) it will draw power from the capacity and thus deplete the batteries charge and you can watch the number next to the battery. Even if reinforcement is not being used it will trickle away to uselessness. Got to pick and choose when to use to maximize benefits.
Rechargeing it requires the presence of excess power ( ie turn shield reinforce OFF and slow down until there is excess power) just wait, it will slowly recharge. Take a mauler in single player and practice to get the hang of the timing.
Use of battery power falls into the "use your tractor dam-it" phrase from SFB , though "Speed is Life" is more well known.