Who ruled them and how were they appointed? Was it a permament position or for some finite term? What happened if someone refused to step down? How did the Imperial administration work in provinces?
When? I don't generally like to be that guy and ask users to become more specific with their questions, but this answer is very much dependent on the period in question--provincial administration could and did change completely several times, often within a single lifetime. To a lesser extent it also depends on where--Imperial and Senatorial provinces during the Principate were administered quite differently, and during the 50's, B.C. you had several provinces which, though their governorships worked more or less the same, had different systems of tribute and taxation. When you say the "Roman Empire" are you only referring to the period of and following the Principate?