Without going into a lot of detail that you can
find elsewhere, here's the short answer:
Vegetable oil in it's raw form is composed of molecular chains of fatty acids (ester) and glycerol (sugar alcohol). Exposing the oil to a solution of alcohol such as methanol (from natural gas) or ethanol (grain alcohol), and a strong base (potassium or sodium hydroxide [lye]) results in the chains of molecules "unsnapping" or disconnecting from one another. The glycerin, being heavier, sinks to the bottom of the reaction vessel, and the ester, composing about 80% of the volume floats to the top and is harvested as fuel with only a minimum of further processing (heating and washing with water to remove the alcohol and perhaps some pH correction with an acid to neutralize any unreacted lye).
The result is pure Biodiesel. It's pretty hard to mess it up, even garage brewers can crank out ASTM grade fuel using basic tools.
People who run SVO/WVO say "Why bother removing the glycerin?" and simply filter the raw oil and drive on it. I've already expounded on my thoughts on that subject. I also don't have any stomach for digging around in nasty, smelly grease dumpsters to get the raw materials.
It's possible to make Biodiesel from nearly any fatty oil, all grain and bean crops, palm oil, squashed hogs, turkeys, fish, etc, even algae. Not all sources make the best fuel, though. A 100 million-gallon-per-year plant recently opened in Gig Harbor, WA, processing imported palm oil. Problem is, Biodiesel made from palm oil is a solid at room temperature, making it a bit difficult to use in automobiles. The product the plant makes is intended to be a replacement for bunker oil in industrial plants, and I hear that they have a fat contract supplying cruise ships, which are effectively floating factories, and can keep the fuel tanks heated with live steam 24/7 to maintain the fuel in a liquid state.
Some time back we had quality problems from some turkey fat Biodiesel we purchased from World Energy. Many of our customers had fuel filter plugging issues, and we ended up paying quite a tidy sum out of pocket for repairs to not only passenger cars, but some long-haul diesel trucks in fleet service that were stranded from filter problems. World Energy didn't make good on the fuel, dispite the ASTM certification, saying that it was intended to be blended with petroleum diesel, and not used in concentrations greater than 20%. We got bit big time on that one, another reason that we are expanding our production facility to 5 million gallons. Better control of the finished product.
We see a lot of confusion between SVO/WVO and real Biodiesel in the general public, a perception that most media coverage doesn't address adequately. We also find that most media likes to play up Biodiesel users as oddities and quirky tree huggers, attempting to capitalize on the "human interest" angle and usually succeeding in making users look like misfits of society. It has been a long haul to build a company that has mainstream recognition, but each day brings us closer to "normalcy" in the realm of motor fuel creation and consumption.