And I’ve been ignoring it for a while. But I’m terrified that one day someone’s going to flick cigarette ash at my car and the whole thing is going to go up.
So my question is what will it take to repair this thing? Is it the sort of thing that takes professionals and lots of money (which I don’t have)? Or can I just slap a piece of duct-tape over the leak?
You didn’t really give us much to work with. Is the leak coming from the back or front of the car? Is it leaking externally? Or leaking inside the car? Is the gas coming out of the glove compartment? Or the heater vents? Is it leak only with a full tank, or all the time, car running, or shut off? We need a little more info. It could be a major repair (bad fuel tank =$300+ repair) or something as minor as a bad fuel line or loose connnection which could be repaired for $50 or less. If I were you, I might stay away from the duct tape repair. As good as duct tape is for fixing many things, I doubt duct tape and gasoline are a very good mix.
Ok. Here are some more details (I figured a leak is a leak is a leak. Shows what I know!): There is a strong smell of gas about the car, and I noticed that it’s dripping from underneath the car. I think it’s coming from near the front. It appears to be leaking at all times. The smell of gas is strong enough to give me a headache, and the car leaves a little puddle everywhere it goes.
And the duct-tape thing was a joke. 
The fact that your leak seems to be coming from the front of the car and not the back probably means it is not your gas tank leaking. It could be something as simple as a fuel filter cracked or line loose, or a leaking injector rail. I’m afraid you are going to have to open the hood to solve this one. Poke around with a flashlight. If it were me, I’d park it without driving it another second, because it might be more than your own car that goes up in flames, if you are parked near something expensive, you (or your insurance guy) might be buying someone elses caddy or lincoln, or something.
All visible gas leaks are seriously dangerous. That said get this car to a mechanic. Really no matter how busted you are for cash. The reason I say this is you do not want to geuss about where the leak is. If it is this bad anyone could trace the leak with experience for 10-20 bucks. Maybe you could fix that or not. But driving a gas bomb is not what you want to do. Duck tape is not a funny answer for this.