Generally, I tend to stick to earlier periods, but this is a developing area of interest to me. Here's what I can tell you.

By the end of the fourth century, Roman urban life was on the decline. Roving bands of bandits plagued southern France and northern Iberia (a problem that had evidently existed even back in the second century, if Apuleius's Metamorphosis is anything to go by), and the cost of maintaining infrastructure was becoming too great. The Crisis of the Third Century had seen the collapse of Roman rule in many areas, and Constantine had only just begun to restore it. The old system of slave farms had begun to decline in favor of tenant holding. Generally, the Roman world was in a state of either stagnation or decay for many reasons, including the radical changes to the Roman constitution made by the Severan dynasty and increasing dissatisfaction of the provincial elites with Roman rule.

These new "barbarian" kingdoms generally kept the old Roman administration in place, at least initially. For the most part, this was for practical concerns: these men went from being the leaders of tribes and warbands to governing cities and wide stretches of territory. They kept in place municipal and local talent, governing indirectly from their capitals (the Franks at Paris, the Visigoths at Toledo, and the Vandals at Carthage). That said, they did not go around tearing down aqueducts and bath houses (though many were stripped of their finery). Life went on just about the same, except that instead of a governor appointed by the Emperor at Rome, it was a Germanic overseer appointed by the King at [insert name of capitol here].

Something important to talk about is religion. Most of the Roman population was Chalcedonian Christian in nature, as opposed to the Arian Christianity of the Germanic invaders. This proved to be a major sticking point in relations between the locals and their new Germanic overlords, preventing very strong integration between the two groups. The Franks were even more alien, being Germanic pagans until Clovis's conversion in 496, which resulted in the mass conversion of the Franks to Chalcedonian Christianity. The Visigothic king Reccared was famous converted by Isidore of Seville in 587. The Vandals, however, did not repudiate Arian Christianity and persecuted the Chalcedonians, which was part of the reason that their rule in North Africa collapsed so quickly when the Byzantines invaded.

Literary culture continued to survive largely thanks to the Church. Bishops like Gregory of Tours and Isidore of Seville, as well as the abbots and monks of numerous monasteries, preserved ancient works and penned new books. Isidore of Seville's Etymologiae is an important source of otherwise lost classical texts, while Gregory of Tours provides our best source for the early Merovingian kings.

In some ways, life for the average Roman even improved underneath the Germanic invaders, since their tax money was no longer being sent to Rome to support a dying metropolis. The new populations helped to revive and repopulate the countryside, while the Germanic warriors helped provide greater levels of security to the regions that they conquered in a way that the legions simply could not.