I will unload what little I know about this. It's mostly speculation, which is about all that historians can do with regards to this period.
The last hurrah of
Mycenaean (aka
Achaean)
Greece seems to have been the
Trojan War, which took place somewhere around
1250 BC. Around 1200 BC, a series of events caused Mycenaean civilization to fall apart. The warlike Achaeans may have exhausted themselves with the effort spent in the Trojan War; the changes wrought by the eruption of
Thira around 1400 BC may have made cities untenable.
However, the most common explanation for Mycenae's disappearance is that a northern tribe of Greeks, known as the
Dorians, invaded and overcame the Achaeans.
Homer's
Odyssey may contain an echo of this invasion; when
Odysseus returns home to
Ithaca from his twenty years of travels/travails, he finds his house full of ruffians eating him out of house and home: the suitors of his wife
Penelope. Although Homer states these to be Ithacan noblemen, Ithaca is a small place, and might not have been able to support that many noblemen. Perhaps one of the
bards singing the story as
oral tradition during the Dark Age changed it so as not to offend a Dorian overlord.
Another interesting speculation concerns the whereabouts of the Achaean Greeks after the Dorian invasion: At about the same time, raiders known as the "
Sea Peoples" began to terrorize the
Levantine coasts of
Anatolia (
Turkey) and later
Israel, where they eventually settled, and were given the name of
Philistines by the writer(s) of the
Bible. It is widely considered plausible that these Sea Peoples/Philistines and the fleeing Achaean Greeks were one and the same.
There appears to be very little in the archaeological record about life in Greece during the Dark Age. However, around 750 BC, sheepherding settlements began to form back into cities, and writing reappeared. It was also about this time that the
Iliad and the
Odyssey were written down. The period of history we call
Classical Greece had begun.