One method is the use of an inverter, which uses automotive 12V DC to create a 120V/220V AC and emulate an in-home plug. Inverters are consider to be inefficient. Thus, a variety of DC-to-DC voltage converters have been created so you do not have to use an inverter.
One significant plus to inverters is that they are inexpensive and readily available. Inverters can be purchased at nearly any computer or electronics store, as well as hardware
stores, auto supply stores and even large discount stores like Wal-Mart.
The major downside to using an inverter is inefficiency. Consider that the vehicle supplies
to the inverter. The inverter converts that to AC power. The computer power supply converts that back to DC to power the computer. The amount of energy wasted doing a double conversion like this varies from unit to unit.
Another drawback to inverter usage is heat. The process of converting DC power to AC power generates heat. This presents a potential safety hazard. Too much heat could result in a fire. Most inverters have a heatsink as part of the casing, but still get quite warm.
The design of some inverters can cause electrical noise due to the way that the 12V DC is stepped up to 120/220V AC. This can give you what is termed "noisy" power. You then feed this "noisy" power to your PSU which inturn supplies power to your computer and it's audio card. It is very difficult to remove this noise from your audio signal. This problem is more noticeable in cheaper inverters. Usually the more expensive the inverter, the better they are designed to combat this noise.
Inverters are also more prone to EMI, or electromagnetic interference. EMI can induce 'noise' into an audio signal, resulting in a static humming, which nobody wants to hear for hours on end during a cross-country road trip.