This is a rather complicated question. The period of intervention in Judaea under the Republic is confusing and a little unorthodox, no pun intended. It starts in 63 when Pompey, recently victorious over Mithridates and busy setting up the new Roman province of Syria, gets involved in the Hasmonean succession war. To keep things simple, the behavior of one of the claimants, Aristobolos, pissed Pompey off and caused him to directly intervene with military force. Jerusalem was put under siege and eventually sacked. In the aftermath, Pompey saw to it that the Hasmonean kingdom was partially dismantled. While Hyrcanus II was nominally supported, he was reinstated only as high priest and not as ruler (he would later be made ethnarch, a sort of ruler in Greek style, but that's not important here). The direct territory under Hasmonean hegemony was severely reduced, including coastal access. Jerusalem was now loosely and rather unofficially integrated with the new province of Syria, and was administratively beholden to the Roman governor there. This meant that they paid taxes and suffered the same obligations as other Roman subjects, though in this case it was ad hoc. And to top it off, several Hellenistic Greek cities of middling power were set free of their obligations, eventually to form the federation of ten cities in the region called the decapolis. They were free to govern their own affairs but ultimately under the Roman thumb. The sum of all this was the rather harsh reduction of the importance of the Hasmonid state both politically and economically.

Our sources suggest that Hyrcanus II was ineffectual and weak, and had been manipulated by another figure, Antipater I "the Idumaean." He was a professional kiss-ass and steadily ingratiated himself with the Romans. When Caesar found himself hemmed in the palace at Alexandria in 47, Antipater organized a "rescue" and earned Caesar's fondness. This all culminated with Caesar naming Antipater the first procurator of "Iudaea," the first precursor to the later provincial territory. The word "procurator" is problematic for this time period and a little difficult to explain in legal terms, but let it just be said that Antipater was made the head honcho, with ties to Roman government. I myself am not sure if he was technically under the authority of the governor in Syria, or if he "reported" directly to Caesar. It is one archetypal example of the type of administration which will be familiar under the Empire, of Emperor appointing personal lackeys to positions of power in smaller provinces (those are actually officially called procuratores, when civilians, or prefects when military-oriented).

Antipater's son was the famous Herod, who was awarded with the title "King of the Jews" in 40 BCE. Like his father, he was technically obligated to the Romans, but also enjoyed autonomy. Under Herod's ministrations, the powerful port of Caesarea Maritima was founded. But when Herod died in 4 BCE, his "kingdom" was divided among his sons in a complicated division of territory. I'm not even sure I have it straight myself. The Romans quickly became unhappy with this situation and, from 6 CE onward, "Judaea" (including Judaea, Samaria, and some other places) was governed directly by Rome. More specifically, it was deemed an "Imperial" satellite province of the Syrian governmental district and was controlled directly by the Emperor via his chosen agents, called either procurators or prefects (the are essentially the same) of the equestrian social rank. If that sounds confusing, that's because it is.

This situation lasted for about 30 years, during which time the Jews were in theory autonomous and were able to decide many of their own court cases according to their own laws (for instance). But for a brief interlude, 41-44 CE, Herod Agrippa was affirmed as a new "King of the Jews." It does not seem that the Romans ever intended to award the Jews full autonomy again, however. After 44, the area is again ruled by an Imperial representative, now officially called a "procurator" as part of the Emperor Claudius' administrative directives.

In 66 begins the "great revolt," which lasts until 70 CE. When put down, the governing returns to the hands of a military-minded representative (an Imperial legate), though Herod II was on the scene and "king of the jews" in some capacity until 94 CE.