You never, ever want to hard-wire things like this to your car battery. First, it would mean the camera is on all the time and could possibly drain your battery. Second, it's a fire hazard. Third, it's just impractical! Most cars have a fuse box somewhere inside the cabin that is readily accessible.

Your car also has electrical circuits that are "hot" only when the car's keys are turned to the 'on', and 'aux' position. One of them is the radio, so this is a prime circuit to draw power from for a dash cam and is the one I would recommend.

You can buy these "fuse taps" (http://www.amazon.com/Bussmann-BP-HHH-RP-Circuit-Converter/dp/B004AHADOC) that go into the fuse slot for your car radio. You then put the radio fuse into a slot on the fuse tap, and add another fuse for the new circuit we are creating (10amps is good for this application). Keep in mind that there are a few types of fuses out there. The fuse tap I linked to in the first sentence is for a mini fuse, which is most modern cars. Here is the wiki article on car fuses.

So now I have an extra wire coming out of my fuse box. It's a 12 volt DC power source that is on whenever the car is on. You'll need to convert this 12VDC power into 5VDC, add a power connector for the dash cam (generally mini-USB), and add a ground.

For the ground, watch this video and skip to 1:19. Basically just find a black wire nearby that you know is a ground, and use one of these to tap into it.

Last is converting the 12VDC from the fuse tap to a 5V USB connector... I used one of these. I bought it, along with everything else on Amazon and it all came to less than $30. Took me about 30 minutes total installation and I'd be willing to help you with anything vehicle specific (just PM me).