Depending on where you are in the empire the first period of stability would be immediately, as the local tribal power structure Rome suppressed would come back to fill the void. Elsewhere in the empire the local politicians and military leaders would simply resume control of the areas that they already controlled.

An important thing to know is that the Dark Ages do not refer to a total collapse of society into anarchy and barbarism, that was once thought but modern historians greatly disagree, instead the dark ages are dark in the sense of a lack of information. Many of the people’s of the dark ages were illiterate and did not have the kind of sprawling bureaucracy that Rome had generating 1st hand written accounts.

Italy in time would break apart into small regional powers with local land owners taking control of whatever territory they could call their own. There are many land disputes during this time as the central bureaucracy had fallen. But in general feudalism takes full hold as the land will become divided, occasionally brought into a larger state before falling back to the local lords.

In the immediate aftermath of the sacking of Rome it is important to remember that Rome still existed, the Eastern Roman Empire would remain an empire throughout the entirety of the middle ages until the start of the early modern period (in fact being one of the things that distinguishes when the early modern period begins)

In 476 Odacer, the first barbarian king of Italy, declared himself King of Italy. You can read more about this here: https://www.britannica.com/biography/Odoacer

Most of Italy would be brought under control of the Ostrogoths as the Ostrogothic Kingdom until being conquered by the Eastern Roman Empire in 533.