Precious metals are those metals that have high economic value such as gold, silver, platinum and palladium. These are typically mined from sources around the world. The metals are then extracted from the ore (which contains both the precious metal as well as other substances) by chemical or mechanical means. Some metals exist in the ore in the elemental state while others are in the form of a compound so a chemical reaction is needed to extract the metal.
Regardless of many attempts, alchemy (chemical reaction to change the identity of an element) doesn't work. However, we can produce precious metals from the products of a nuclear reaction which can result in the change of an atom's identity.
A variety of factors including amount needed, cost, availability, environmental impact, and ease will determine the best method for a particular metal.