This demonstrates how I made a basic setup for casting, and can also to some extent be used for blacksmithing.
Let me state a disclamer that I know almost nothing about blacksmithing and most of my knowledge thus far is from research and not experience. The processes and materials presented and resulting from the information I am sharing are potentialy lethal. Please consider this as a primer to get you interested and demonstrate how simple it is to make the necessairy items for forging and casting. Do, however, search elsewhere for more information before undertaking any projects.
For the burner you need 1 and 1/4 inch pipe fittings: two T's, two full-thread nipples, one 3" long nipple, two caps, a reducer that goes down to 3/4" and a 3 inch long 3/4" nipple.
Fit everything together as shown with a couple pipe wrenches except the top cap. Drill a hole for the oil line. Test it to make sure it's working the way you want it to. Then encase it in fire clay. (see next step)
For the oil line I've just used some 1/4 brass tubing I had but steel brake line would be better. I fitted this to a valve and the valve to a tube going to my oil container. So far my container is just a can with a copper coupling for a hose in the bottom.
For the forced air I took a small vaccuum and duct-taped a tube to the air exhaust, the tube is about 20" long. Then I use a pipe clamp to secure it to the burner. Eventually this will be replaced by a small squirrel-cage type blower.
To run the burner I first start a wood or sometimes charcoal fire in it. Just get some small chunks of wood and fill up the main section of the burner. Once it's burning well put the cap on and connect the blower, turn it on as low as you can. Turn the oil on to a very slow drip, it'll probablly get really smokey for a bit. If the flames go out back down the air input or throw in a couple more peices of wood. As the burner heats up try turning the blower on higher, work gradually until there is a steady bright yellow flame comming out of the blower. As the air is turned up you'll have to open the oil valve more. On a full blow oil will have to be streamed in steadily and excess will fill the bottom and leak out the air input. Just catch this with a cup and pour it back into the oil container.