How to make artificial diamond?
First off, take a look at the Wikipedia article: Synthetic diamond. Basically, there are two ways to artificially generate the heat and pressure needed. First is the "conventional" high-temperature, high-pressure method, which uses a press to put a sample of pure carbon graphite under pressure of about 5 gigapascals (1GPa = about 10,000 atmospheres or about 145,000 psi) and about $\pu{1500 ^\circ C}$. This combination encourages the flat hexagonal lattice structure of the graphite to morph into the trihexagonal 3-D lattice of diamond. Second is the chemical vapor deposition method, in which a substrate of diamond crystal is exposed to sublimated carbon plasma (temperatures exceeding $\pu{3000 ^\circ C}$) in a hard vacuum (less than .0001 torr). The sublimated carbon attaches to the crystal substrate, "growing" it.

Both of these can be used to create so-called "memorial diamonds" from the cremated remains of a human. To do that, first the ash is chemically filtered to separate the carbon from "pollutants" naturally occurring in the body that don't combust into gaseous substances during cremation, such as calcium, phosphorous, iron etc. Then, this "amorphous carbon", much like any other carbon, can be used in HTHP or CVD processes, along with additional carbon as may be required to grow the diamond to the proper size. Usually, the HTHP process is used, as it makes the best use of the available carbon (CVD requires sublimating a lot of carbon, more than would be left behind in the ash, and most of which ends up on the chamber walls and not the substrate), and requires less energy (it's easier to maintain mechanical pressure once applied than to maintain temperature).