It also comes with a power adapter, into which the FireWire cable plugs. (There's actually a female FireWire port on it.)
The dock is just extra. The USB2 or FireWire cable plugs into the back of the dock, and the iPod is inserted into it. It does the same thing as plugging the iPod directly into your computer does, except also has a Line Out jack on it, so you can hook it up to a stereo.
For your problem, though, all you really need to do is buy a car charger.