How can families assimilate to a new culture?

The first step is to want to. The second is to master the predominant language. While reading about the history of a nation is helpful what's more important is understanding the laws so you don't erroneously end up in jail. After that it's a matter of studying those around you. What are their goals and priorities? This will vary sometimes by block so decide which part of the new culture fits you best and work on becoming that. If you're in a small town in Alabama the social morays will be different than if you're living in Upper West Side Manhattan.