Flamethrowers on cars are pretty common:

They are sometimes added for defensive purposes, as seen in this CNN story:

This, however, is probably the ultimate, with flames going 20 or 30 feet into the air:

So how do they do it? In the simplest kits, you fit a spark plug on the tailpipe and light gasoline that is coming out in the exhaust. No properly tuned modern car with fuel injection and a catalytic converter has any fuel leaving the exhaust pipe, but older cars with carburetors can be set to run rich, and there is lots of fuel to burn. The spark plug simply ignites it to create the flame.

To get the bigger flames, you have to pump in extra fuel into the exhaust stream. Here you can see one possibility – a propane tank in the trunk:

The car with the 20 foot flames is using a pump to squirt streams of gasoline (or some other flammable liquid) out the back. (on this page, the preferred fuel for the flamethrower is denatured alcohol solvent).