First, a kiln or furnace is needed. It must have the ability to generate enough heat to melt small qualities of metal. According to researcher Mike Leahy, gold melts at 1,943 degrees Fahrenheit. E Prospectors recommends that your heat supply be above this, at a temperature of 2,552 degrees Fahrenheit, to fully melt the silica sand and other fluxes. Furthermore, it will have to hold this heat for about one and a half hours. Many designs of kilns are readily available, using a variety of fuels such as coal, acetylene, or propane. These furnaces do not have to be large. To smelt small quantities, a simple acetylene torch and a small crucible is all that's needed.
Flux is needed. Flux is a compound that, when heated, will draw all the impurities out of gold. Flux is made out of borax, silica sand, soda ash, and sodium nitrate. Silica sand is common playbox sand, and is available at home improvement stores. Clear bottles are also made out of silica sand, so broken up fragments from glass bottles will work too. The other chemicals are common, and available at any chemical supply house. Borax is used for laundry applications, and available at any grocery store.
Place the mixture with your crude gold in a small crucible, and heat the mixture. When the mixture has melted thoroughly, pour it into a mold and allow it to cool down. If the mixture is too thick, add a little more borax to thin it out. When the pour has cooled down, break the mold open and separate the gold from the glass-like flux.
Bear in mind you are working with very hot objects. Safety should always be a priority. The GGPA recommends not working over concrete, because the concrete will explode if molten metal accidentally falls on it. Furthermore, protective heat equipment should be worn, such as gloves, face protection, and body protection.