There are many ways that newcomers can become acculturate into a new society. There are two words, that people often use interchangeably, that are associated with the ways that people acculturate: assimilation and integration. Despite the fact that they are often used interchangeably, they do not mean the same thing. Assimilation implies gives up aspects of your culture to become part of the dominant society. Integration is defined as a two-way process in which newcomers and the dominant culture come to become more alike. In other words, assimilation requires newcomers to change whereas integration, at least technically, suggests that both newcomers and the dominant society change.
In the United States, there is a long history of institutions, government and non-governmental, that have encouraged newcomers to assimilate. Moreover, if they refused, to give up their culture, they were seen as either stubborn or incapable of fitting in. At the same time, there is has been another, less formal, tradition of integration in which the dominant culture adapts and even begins to take on words, customs, and foods from immigrant communities.
This segment from the PBS series The Italian Americans reveals the pressure on Italian immigrants to assimilate.