The Early Middle Ages in Europe saw a large number of short-lived monarchies and a few long-lived ones. The Catholic Church rivaled and often surpassed secular states in its power. Throughout the entire middle ages, for most of the peasantry, interaction with the state in the broadest sense that we have today (i.e. with the king) was scarce. Local rulers, dignitaries and institutions, had large autonomy and more direct influence on the daily lives of peasants.
Free cities are a good example of completely autonomous sovereignty. If they were chartered, the local princes had little power over them - but chartered cities only appear in the very end of the dark ages.
Anyway, I recommend 'Medieval Cities: Their Origins and the Revival of Trade' by Henri Pirenne. It's an old book and there's definitely more up to date research, but Henri Pirenne is a brilliant historian and writer and he paints a very vivid picture of what the "so-called dark ages" in Europe were like.
As the old structures collapse, a new order invariably claws its way out of the debris. These are periods of tremendous innovation and creativity, here boosted by the prosperous Medieval Warm Period.
The "dark" in "dark ages" reflects more our lack of written documents from these periods (little surviving literature) and a sentimental bias of the early historians toward the lost Roman period. Not a lack of stuff happening -- quite the contrary.
http://www.carrollquigley.net/books.htm
http://www.carrollquigley.net/book-reviews/history_freedom_w...
Oh, and Durant's "The Age of Faith" is also worth a read.