Before you commit yourself to a carbon-neutral fuel source, you need to make sure you can actually get your hands on that fuel. While a grease car will still run on regular diesel, it's pointless to go through the conversion if you're just going to end up using regular fuel.
Most restaurants will have waste vegetable oil (WVO), and most will be happy to give it to you for nothing since they typically have to pay to dispose of it. The better the oil quality for cooking, the better it is for your engine, so start with the more expensive restaurants and caterers and work your way down from there. Just ask to speak to manager and see if you can take the oil off his or her hands. You can use the hydrogenated stuff you'll find at most fast food restaurants; it's just not ideal.
Once you know you've got an easy, nearby vegetable oil source, you can commit to driving a grease car. The first thing you need is a diesel vehicle (the conversion won't work with a gasoline engine). If you've got a diesel car or truck in your driveway, you're all set. Otherwise, you need to buy one. Buying a new one is slightly more complicated than buying a used one, because some states' emissions laws make diesel vehicles less common. Changes in the sulfur content of diesel fuel are starting to change this, though. In any case, getting your hands on a used diesel car is a cinch. Volkswagens and Mercedes have a lot of diesel vehicles out there, and many American carmakers make diesel versions of their pickups.
With a car on-hand, you're ready to convert it to a greaser. You can buy a conversion kit (about $1,000 to $1,500) at lots of online or brick-and-mortar retailers. The conversion basically alters the engine so it has an extra fuel tank and line and injector for the vegetable oil. The engine will take some diesel from the regular fuel line during start-up to get everything warmed up, as well as during shut down to flush the vegetable oil out of the engine. Otherwise, it uses the vegetable-oil fuel line. You can install the conversion kit yourself if you know cars, or pay about $1,000 for a mechanic to take care of it.
With the engine ready to run on grease, you're almost done. Owning the car requires some additional equipment and effort -- not the least of which is figuring out how to safely maintain a car that runs on a non-EPA-approved fuel source.