you should start by reading
how can I use a laptop as a carPC?
as for your power needs; you should use a DC-DC power supply (don't use an inverter). for a laptop, you only need to provide a single voltage (the power circuits inside the laptop then split/regulate each power rail). you can use a nice universal laptop DC-DC power supply like a carnetix or you can use a cheap auto/air adapter from eBay.
for your power connections, read the
Hooking Up Your Power Supply in the Car FAQ.
good luck
