biodiesel is actual diesel fuel, made by a chemical reaction involving lye, vegetable oil, and (usually) methanol. There's a chemical name I don't remember. I'm running my car on that now. It requires no conversion whatsoever. In fact, biodiesel is not only a fuel, but a solvent, and will burn cleaner in your engine, and has a higher level of lubricity than diesel, so your engine will run smoother. Emissions are much cleaner than even a hybrid. You can switch back and forth between diesel and biodiesel without a care in the world.
You can buy biodiesel in some places, or you can make your own, if you have a source for methanol and vegetable oil--either new or used.
You can also run a diesel engine off vegetable oil, either clean or used. For used oil, you have to filter it, and you have to convert your tank system. Most cars (except one or two) require two tanks. You have to start the car on regular diesel, then switch it to oil, then switch back to regular just before you shut it down. If most of your trips are short ones, this isn't worth it. The conversion also requires a tank heater, because the oil has to be heated enough to melt the trans fats.
With clean oil, what they call SVO, you don't need the tank heater (though it wouldn't hurt), but you still need the dual tank system, except on a few cars (old Mercedes five cylinders fromt the 80s being the main one).
You can find conversion kits for these vehicles, and they don't require too much to be done to the car. Look up greasecar and greasel, for instance.
This vegetable oil conversion still lets you run regular or bio diesel with no problem.
That's an overview. There's a ton of research on the net, and it's been done for decades, and it is somewhat common in Europe, so there's nothing experimental about it. Google "biodiesel" or "WVO" (waste vegeteble oil) or "SVO" (though you'll get a lot about mustangs and tauruses with that one). I don't have my bookmarks on this computer, or I'd give you a few links.
There's one other method, of mixing SVO with some type of fuel, like diesel, or kerosine. This supposedly gums up some engines after a while, though there is much debate.
Here are two links:
http://journeytoforever.org/biodiesel.html (this has lots of info on SVO and WVO as well. Search around the whole website)
http://www.biodiesel.org/