We have observed the development of the surfaces during gas-source growth of silicon and germanium in an elevated temperature ultrahigh vacuum scanning tunneling microscopy (STM), with near-atomic resolution under a range of temperature and flux, which are the two dominant parameters, and applied atomistic modeling to the structures seen by STM to enable us to give confident interpretation of the results. A key role in the growth of silicon and germanium on Si(001) from disilane and germane, respectively, is played by the surface hydrogen. The growth of germanium follows a similar path to that of silicon for the first few monolayers, after which the strain becomes relieved by periodic trenches, and eventually by a combination of faceted pits and clusters, both of which nucleate heterogeneously at surface defects. Understanding these processes is crucial to controlling the self-assembled Ge/Si quantum structures.