Diamonds are the high-pressure form of carbon and are produced deep within the earth's mantle, more than 150 kilometers beneath our feet. They have been sought by man for the past two millennia. Diamonds occur in primary (hardrock) and secondary (alluvial and marine placer) deposits. Although diamonds can be found in rocks as varied as high-pressure metamorphic garnet-biotite gneisses and meteorites, the only economically significant primary source rocks known to date are kimberlites and olivine lamproites http://www.empr.gov.bc.ca/Mining/Geoscience/MineralDepositProfiles/ListbyDepositGroup/Pages/NCarbonatites.aspx.
Both of these rock types form as magmas deep in the mantle and rapidly rise through it, sampling diamonds along the way. It must be stressed that diamonds do not form in the kimberlite or lamproite, they are simply transported to a level within the earth's crust where we can access them, by these magmas. As exploration continues, new economic deposit types may be found.
Diamonds and the rocks that host them have fascinated both exploration geologists and scientific researchers for decades and there are literally thousands of scholarly publications concerning them. Rather than reproduce some of this information, we refer you to an extremely informative site that give good overviews on diamonds and diamond geology:
Diamond exploration generally involves a combination of techniques that first lead one to the potential source rocks (generally kimberlites or olivine lamproites) and then test their diamond content.
Kimberlite indicator mineral sampling is one technique commonly used, that is specialized to the hunt for diamonds. When kimberlite is weathered and eroded, the more resistant minerals within it are dispersed in soils, stream sediments or glacial sediments. Some of these resistant minerals are also characterized by high specific gravity (i.e. are heavy) and are therefore easily extracted from the more abundant, lighter minerals in the sediments by gravity separation. Important kimberlite indicator minerals are pyrope garnet, eclogitic garnet, picro-ilmenite, chrome spinel (chromite), chrome diopside (a clinopyroxene) and, of course diamond. However, these other minerals are much more abundant in kimberlites than diamond and therefore are often easier to find once the kimberlite has been weathered. In non-tropical climates, olivine can also be an important indicator mineral. Some of these minerals have distinct colours that aid in their identification: pyrope garnets are a rich wine-red or lilac colour and chrome diopside is a bright, vivid green. The presence of these minerals in sediments suggests that there may be a kimberlite in the vicinity.
The chemistry of the indicator minerals is also important. Researchers have analyzed pyrope garnets, eclogitic garnets and chromites that occur as inclusions within diamonds and found that they have distinctive chemistry. Pyrope garnets that formed with diamonds are often referred to as G-10's. Therefore, by studying the chemistry of these minerals found in exploration samples, one can determine if they formed within the same region of the mantle that diamonds form. If so, the kimberlite that brought them to the surface may have also transported diamonds. A study of the chemistry of picro-ilmenite tells us something about the nature of the magma that potentially transported the diamonds, if it would have preserved or destroyed the diamonds during transport.
Other exploration techniques, such as geophysical surveys (magnetics, resistivity, gravity) and drilling to test anomalies are also employed. These techniques are also used in the search for other ore deposits.