Our diamonds are grown using two methods: the Chemical Vapor Deposition (CVD) and the High Pressure-High Temperature (HPHT) technologies.
In the CVD process, a diamond seed (lab-grown diamond dust) is placed in a vacuum chamber that is heated at high temperature and filled with a carbon rich gas. This gas is ionized, letting the pure carbon slowly adhere to the diamond dust, atom by atom, layer by layer, which ultimately culminates in the creation of the diamond.
Regarding the HPHT technique, the diamond seed (also lab-grown diamond dust) is placed on a piece of carbon and exposed to high pressure and temperature conditions. This seed melts with the piece of carbon leading to a larger diamond forming around, that is finally cooled to discover the created diamond.