The cells divide, some to form sperm and some to form eggs. When sperm and eggs join together the resulting cell forms a new, more normal sized frustule. Sexual reproduction seems to occur in other cases as well, but it is rare, and sexual reproduction has never been observed for some species. The question is not where to find diatoms as much as it is where to not find diatoms. They are certainly abundant in both freshwater and marine habitats.
Diatoms are also abundant in soil and have even been gathered from air samples.
Because of their ubiquitousness and the many possible variations in the structure and sculpturing of frustules, there are many thousands of described species of diatoms, and probably many more that are not described. Among the algae, they are one of the more difficult groups to identify to species, and even determining the genus can be difficult. A good microscope is a prerequisite for any attempt at identification, and even then a good dose of experience is needed. Of course, one does not have to identify these masters of glass to appreciate their beauty. Personal advice and service.