Here's my experience using a device called a DC inverter to produce AC power from a car battery:
First off, in my opinion, every vehicle should have an inverter. They should be standard in all cars and vans. They cost $60 to $100 and using one you can run just about any AC appliance, including a TV and VCR (I ran a color TV and VCR off a motorcycle battery for 3 hours, and the battery didn't die, I got bored), whatever. I don't know why cars don't come with them as an option. I suppose they will.
An inverter is a device with a chord that plugs into your cigarette lighter, and the chord goes to a little box with a switch and an AC outlet on it. Plug it into your cigarette lighter, turn it on, and voila, a mobile AC outlet, no more need for the power grid.
You can get inverters at Radio Shack and now, given the ubiquity of laptop computers, computer stores are selling good and cheap models for people to power their laptops directly from their cars without having to order an overpriced model-specific cig lighter adaptor for their laptop. You can also get inverters at truckstops, though they tend to be high capacity so truckers can run their air conditioners and etc. You probably don't need a high capacity one.
Each inverter is rated for how many watts it can handle. Unless you're doing serious stuff you won't need more than the entry level 140 watts, which is about 1 amp at U.S. rates of AC electricity (remember W=VA, or watts = volts x amps. so 120 watts = 120 volts times 1 amp, or whatever. When they rate the inverter at 140 watts, they are truncating the sentence "140 watts at 120 volts at 1 amp"). The rating is for continuous power (steady stream of AC at that wattage) and power in bursts (short blasts of higher wattage). My 140 watt continuous can handle 400 watts in bursts such as a powerdrill would produce, though I've never tested the bursting power.
I have the little Radio Shack inverter that does 140 watts. I love it. I also have an inverter made by Tripp Lite, but I hate it it's rated at 300 watts and has two outlets, which is nice, but it has a fan which is always on and it's noisy and it whistles every time I turn the ignition. I would recommend against a fan unless you're planning on doing serious inverting.
I connect my inverter straight to the battery using one of those devices sold at radio shack with the female cigarette lighter attachment on one end and positive and negative clips that attach to your battery on the other.
Most inverters claim to shut off when your battery goes below 12 volts so you can't run your battery dead, but don't you believe it.
One thing about inverters though is they don't produce perfect AC current. Certain things, especially non-digital recording gear, will register a hum (though not always), certain other things will get hot. Most things will work fine though. A modem I once had on my laptop hummed and got hot. My new modem doesn't. Who knows why. The reason for this problem, and I only vaguely understand all this, is that AC current is a full sine wave (an endless S centered about an axis), whereas DC current is only the top portion of the sine wave (lots of C's). What an inverter does is invert those C's and offset them, artificially producing a sine wave (S's). I've also heard it said that inverts don't produce smooth sine waves, but instead a "square sine wave". Apparently, some appliances can tell the difference and others can't.
In my '80 vanagon Westfalia (Van Glorious the WryBreadBox) I burn CDs, power my regular ink jet printer, power and recharge my laptop, send emails, etc. etc. etc. I keep an eye on my battery level of course. I have not yet installed my deep cycle marine battery.
This entire message was written powering my laptop off an inverter. If I seemed a little long winded and light headed, blame it on the surf and sunset which are happening like fireworks right outside my poptop's window.