The following resources provide focused reviews of the scholarship relating to various aspects of migration, which can help you understand the context of your research question as well as identify sources for further exploration.
Several subject headings exist to search in the catalog for works about immigration, migration, and immigrants.
The tag for much of the information about immigrants in the census is "foreign born." "This includes naturalized U.S. citizens, lawful permanent residents (immigrants), temporary migrants (such as foreign students), humanitarian migrants (such as refugees), and people illegally present in the United States." (Census web site)
The Census Bureau administers the American Community Survey. Among the questions asked is "place of birth." The Census Bureau provides a chart explaining the tools available to retrieve statistics. Data for analysis with statistical packages can also be downloaded for analysis from the web site of the Interuniversity Consortium for Political and Social Research (ICPSR).
Begun in the 1940s to track employment and unemployment in the United States. The current sample size is approximately 60,000 households monthly. Data are available from the 1960s on. The Bureau of Labor Statistics administers the survey and produces data-based reports on various topics, including foreign born workers.
Other government agencies have "piggy backed" on the CPS through supplementary surveys on specific topics, including immigration. A chart of those supplements indicates the topics, the months and years they were administered, and whether or not the data are available. Data can be obtained via several sources.
Handbook of U.S. Labor Statistics
Compilation of statistical tables, including those about foreign-born population, based on Bureau of Labor Statistics data. Location: Stokes (SPR) and Firestone (F) (call no. HD8051.A63--Current volume in (DSS) Data and Statistical Services.)