Apologies to graydonblair, who wrote this excellent quick guide originally. Alas, it was somehow lost when we made the site switch.
Biodiesel is most commonly made by chemically altering an organic oil
(commonly vegetable oil or lard)
Here's a simplistic approach to how Biodiesel can be made

Click the Link Below for full descriptions on each step in the graphic above.
http://www.utahbiodiesel.org/biodiesel_making.html
Additional Resources:
Here's some really great resources to help get you started making your own Biodiesel.
Collaborative Biodiesel Tutorial - www.biodieselcommunity.org
- Learn the basics of what it takes to make biodiesel here.
Getting Started Making Biodiesel Article - www.biodieselcommunity.org/gettingstarted
- A great article that cover's the things you'll need to do to get started making Biodiesel from waste vegetable oil.
Kitchen Biodiesel - http://www.kitchen-biodiesel.com
- A visual guide to making a small batch of biodiesel
Homebrewing Guide - http://www.localb100.com/book.html
- Maria "Mark" Alovert publishes this guide that is considered by many homebrewers as THE guide to have on hand when making Biodiesel.
Biodiesel Basics Yahoo Group - http://groups.yahoo.com/group/biodieselbasics
- An online Yahoo group completely dedicated to answering any questions you may have on making Biodiesel yourself.
You're best bet to get started is to make a small test batch and go from there! Soon you could be running on a great renewable resource that's fairly inexpensive to make and a whole lot of fun.
Graydon Blair
Utah Biodiesel Supply
http://www.utahbiodieselsupply.com
If you have questions on how Biodiesel is made, please post them as separate threads.