The nature of migration depends on the circumstances that prompted it. Could you be more specific?

Generally speaking, in the Migration Period, a relatively small contingent of mercenaries or raiders would establish themselves in a new region by acquiring land and political influence. Their families could then join them, bringing their livestock and other portable goods. This happened frequently as the Roman Empire declined, and space had to be found for populations moving westward from the Eurasian Steppe.

To start with, I'd recommend Barry Cunliffe's thorough, user-friendly Europe Between the Oceans. Peter Heather's Empires and Barbarians is long, but accessible and well worth the time.

ETA: I've been shamefully vague, here. The nature and extent of migration can be quite hotly contested, hence my asking you to elaborate.