If you're going to have Shimano electronic Di2, you must have the compatible Shimano SM-BCRI Battery Charger to keep it up and running. As the battery is shared between Ultegra and Dura-Ace, this is the same charger for both systems.
The nice thing about the charger is that it's small, like a camera battery charging dock. You plug the charger in, provided you've also purchased the SM-BCCI-2 Power Cable, push the battery in vertically, and the charger does the work. When the charger is working, you'll see a glowing LED indicating it is charging. When the battery is charged, the unit turns off and the light goes out. Pop the battery out of the charger, back onto the mount on your bike, and you should be good for another 1,000 or more miles of effort-free shifting.
You won't damage the battery by either leaving it in too long or popping it in for a partial charge. The folks at Shimano tell us that if you're concerned your battery is low on juice right before you go on a ride, charge the battery for 15 minutes while you kit up for the ride, and you should be good for up to a couple of days.