Hold the PS button for a few seconds, it will pop up some menus and there you'll see how much battery life you have left.

Hmmm. I thought I tried that, but maybe I didn't hold it long enough.

I was starting to think they just didn't include a battery indicator because your battery is always either out of power or almost out of power.

have fun on the dark side

lol, Anyway, sounds like you need a controller dock. 20 bucks and i always have a fresh controller when i play. 

LOL

The battery really does last very little, but don't go spending extra money unnecessarily, it's a waste.
You do have about 6-8 hours of playing time, and you certainly won't play that much without breaks (you really shouldn't). You got a USB cable with it, so just use your port on the PS4 to charge it, or do what I do, and use your smartphone charger. It charges in less than 2 hours. Just get in the habit of plugging it in every couple of days between sessions, and you should never have problems with low battery.

no problem, if you hold the PS button it will bring up a menu, under the menu there should be your avatar and right next to it there is an icon displaying the current charge of the DS4.

Congrats. I love the system already and it's only going to get better from here on out.

Welcome to 1st class.