Between 500-1100, how much did the kingdoms of the British Isles and other former parts of the Roman Empire know about the lifestyle, history, and culture of Ancient Rome, let's say the year 0? I imagine it must have been a lot, but I wonder why Europe wasn't able to put itself together for so long after the fall of the Roman Empire, given that so many people had been exposed to Roman rule.
As I so often comment on questions like these, you might want to narrow down your question to the geographical region encompassing "the West", because the Roman Empire existed throughout most of the Medieval period in Byzantium. The people of the Byzantine Empire lost very little information on "the ancients" and were well aware of the long history of their Empire. I recently wrote a rather lengthy discussion on their opinions on the Decline of the West here which you might be interested to read.
As for how much people knew in the West after the Fall of Ravenna, well, that might be something that I think another expert will be able to answer much better than I.
Edit: also, try to avoid using the term "Dark Ages".
I asked this same question a long while ago and got a lot of great responses.
I recommend the Dan Carlin Hardcore History podcast "Thor's Angels," as he talks quite a bit about this. That is free to download here:
http://www.dancarlin.com//disp.php?page=hharchive
He's also got a multi-part series called "Death Throes of the Roman Republic" that's pretty awesome, too.