Perhaps one reason there are few replies to this thread is because of the danger involved. This is not something that is an easy and safe DIY project. You could very easily injure yourself or even burn your house down. You can also permanently screw up the putter if you do not know what you are doing when you heat up the putter. That being said,
The putter head needs to be removed from the shaft and completely stripped of all paint and other non metallic substances (epoxy, dirt, platting, etc.) The head needs to be bear metal and that is it.
You will need something to hold the putter head while you heat it up.
You need to heat the head, as hot as you can get it without melting, warping, or otherwise disfiguring the surface. The temperature of the metal will be limited by the type of gas used to heat the metal. Propane, butane, acetylene, etc. all have different heat limits that will restrict how hot you can get the putter head. The different temperatures will cause the finished colors to be different. A red hot glowing head will have a different finish than a head that was not heated to red hot. The more heat you use the more chance of screwing up the head. Some professional refinishers have ovens that heat the heads up to specific temperatures. This is how the golden finishes are applied to stainless.
Once the head is red hot or as hot as you would like to get it, you would quench [rapidly cool (red-hot metal or other material)] the head. You can use fresh motor oil, used motor oil or a combination of the two. Many people think used motor oil works best. Many of the different "oil can" finishes are the result of other elements or substances being added to the oil and these elements or substances are kept secrete for obvious reasons. Depending upon the makeup of the "oil" and the temperature of of the head, you could experience combustion of the oil which could result in serious bodily injury and destruction of property.
Once the head has cooled you can remove it from the quenching liquid wipe it down and view the finished product. Once the head has been cleaned you can redo the process again to get a different look.
If you factor in the cost of the gas, the oil, the time, and the risks involved, it is much better to have a professional apply this finish.