The best way to find a diamond is to look near a deep-source volcanic eruption. Diamonds are formed in the intense heat and pressure of the earth's mantle, and deep-source volcanic eruptions tear out pieces of the mantle, carrying them to the surface. There have been no deep-source eruptions since their identification, but diamonds are evidence of their existence.
There are four ways that diamonds are made. The first is deep-source volcanic eruption. All commercial diamond mines find diamonds in places where deep-source volcanic eruptions have happened. These are not the only places diamonds are found, but they are the most lucrative.
The next method is by subduction. Subduction is the process by which one tectonic plate slides beneath another, typically creating mountains in the process. The bottom tectonic plate can travel deeply enough to form diamonds. Once the diamonds are formed, they break off and travel back to the surface. These sites are rare and do not produce enough diamonds for commercial mining, though individual expeditions, such as in the Arkansas diamond mine, sometimes produce lucrative results.
The third way diamonds are formed is by asteroids hitting the earth with enough force and heat to produce diamonds. Many diamonds have been found after impacts and in craters, but none were big enough to be commercially viable.
The last way diamonds are formed is by heat and pressure out in space, and many meteorites that land contain diamonds, but these are also far too small to be commercially viable.