A quick google search got me to here:
It's got pretty good diagrams for the electrical part, I haven't gone through the whole document myself though. I imagine you'd want to adapt this guide to your needs and maybe read other ways people do flamethrowers, i.e. google for "diy flamethrower".
There are also people selling instructions on how to do this on ebay (that's how the person got the info above in the first place). Here's one link, for example:
These are quite cheap, so maybe spending ten bucks on something like this would be worth it.
If you think you have the fuel part covered (e.g. a pressured propane tank and a 12V activated valve, for example --- btw the pressured propane tank sounds very dangerous in case of an accident) then the electric circuit you'd need is like this:
You'll have to figure out a good relay valve to use with propane, something like this might work.
Also, let me say that, in my humble opinion, nobody should be doing this, so if you do, please make sure you're not putting anyone else in danger. In particular, I would not drive with a pressurized propane tank attached to my car anytime there's a possibility of mechanical damage.