Visit the Department of Energy, Energy Explained [1]. under Biofuels: Ethanol & Biodiesel read "Biodiesel" and all subpages.
I have a buddy, Butch, who "makes" his own biodiesel in his basement from waste vegetable oil. Butch has arrangements with several local restaurants to take their used vegetable oil. He processes this oil into biodiesel which he uses to heat his house and run his truck. The process, called transesterification, is shown below. (And, depending on "what the biodiesel was made from it can smell a little like French fries, or Chinese food, or vegetable oil. Most users of biodiesel report that the smell is greatly improved over that of petrol diesel." UT Biodiesel [2])
Butch built his own setup, but you can buy ready-made systems. If you consider experimenting on your own, remember to abide by local rules and follow all safety guidelines.
Not required, but if you have time and interest, check out the Utah Biodiesel Supply [3] site (and source of graphic below). You'll find a many videos and plenty of other good hands-on detail!
Links
[1] http://tonto.eia.doe.gov/energyexplained/index.cfm?page=biofuel_biodiesel_home
[2] http://www.engr.utk.edu/~sae/utfaq.html
[3] http://www.utahbiodieselsupply.com/makingbiodiesel.php
[4] https://www.e-education.psu.edu/egee401/sites/www.e-education.psu.edu.egee401/files/image/lesson09/WVO%20to%20biodiesel_LD.html
[5] http://www.fueleconomy.gov/feg/biodiesel.shtml
[6] http://www.fueleconomy.gov/feg/FEG2000.htm