At the time of the Civil War, the most recent mass immigration had been from Ireland and Germany in the 1840s. These immigrants adjusted to America in ways similar to how other immigrants adjusted. They tried to get ahead economically while, at the same time, typically building communities with other immigrants to provide them with "shelter" from the outside world.
Immigrants tried to get ahead economically in any way they could. They took the hardest and dirtiest jobs. They did things like joining in the California Gold Rush. Basically, they tried whatever they could to get ahead.
At the same time, they built their own fairly insular communities. These communities allowed them to be among other people just like them. That provided them with emotional and social support to help them cope with the problems of poverty and of adjusting to a new country.