You can assimilate into a new culture by learning the language, and cultural differences and getting to know them to assimilate you usually would have to dress like the new culture and act like it
Families can assimilate into a new culture by adopting some of the culture's practices. For example, a family can learn the language of the new country, and take part of its celebrations. The family could also try some fun activities that people in that culture enjoy, or try some of its traditional food.
It is important to remember that assimilating into a new culture does not mean losing one's traditions and culture. Instead, it is learning to appreciate the culture of the other country and taking part in it.