How are chemical compounds named from their respective formulas?

There are a lot of ways! There is a system using Greek roots, that would make H2O dihydrogen monoxide, and there's the Stock system that gives us names like iron (II) sulfate. Various ions have their own names, SO4 (2-) is sulfate, because it's got a sulfur and a certain number of oxygens as opposed to sulfite, SO3 (-). Anything else you need to know?