I understand how military provinces had either a proconsul or propraetor but how were provinces governed after the military expedition was complete? For example, when Caesar took Gaul, he was a proconsul, but how was Gaul governed after he returned to Rome?
I'm a little confused by what you mean here. What are military provinces exactly? There's no such class of provinces in Roman law. Do you mean the Imperial Provinces of the Principate, which housed legions and whose administrators were directly appointed by the emperors, as opposed to the Senatorial Provinces whose administrators were promagistrates (as in the Republic) but (with the sole exception of Africa) did not contain full legions? That system was a result of Augustus' need to maintain strict control on provincial military commands, it did not exist in the Republic. In the Republic provinces were governed and administrated by magistrates with consular or praetorian authority. Initially a complex system maintained the presence of sitting consuls and praetors in the provinces, along with specially-appointed proconsuls and propraetors. By Sulla's time this had been replaced with the institution of regular provincial promagisterial appointments for all consulars and praetorians following the expiration of their year of office. Provincial assignments were given by senatorial dispensation, and could be extended or reduced. All late Republican provinces were administrated by promagistrates, period.