Start by looking at US census records 1900 -1940, which will tell you when the came to the US (not always accurate, but will give you a time frame for looking for immigration records). Censuses will also give you information about their occupations, members of the household, and whether or not they became naturalized citizens.
If you want you can give us their names, approximate birth and death dates, where they lived in the US, and the country they were born in, and we can help you find the information.
Dear Mr. Gardner,
Thank you for posting your request on History Hub!
We suggest that you review these Genealogy: Passenger Arrival List Research Tips and NARA’s page on Immigration Records to learn how to locate immigration information for your grandparents. There are numerous ways that individuals could enter the United States from Europe such as on a ship that arrived at various coastal ports or over land from Canada, etc. Ship passenger arrival lists were a requirement beginning in 1820, but that does not guarantee that person was recorded or that the list still exists. Many of the passenger lists have been digitized and are name-searchable online using Ancestry.com and FamilySearch.org.
Adding to the information from the previous poster, we searched the National Archives Catalog and located the Population Schedules for the 1870 Census, the Population Schedules for the 1880 Census, the Population Schedules for the 1890 Census; the Population Schedules for the 1900 Census, and the Population Schedules for the 1910 Census, the Population Schedules for the 1920 Census, the Population Schedules for the 1930 Census, and the Population Schedules for the 1940 Census in the Records of the Bureau of the Census (Record Group 29) that may contain information about your grandparents Some of these schedules have been digitized in part. The 1940 Census schedules are digitized and available using the Catalog. See NARA’s 1940 Census Records web page for more information. For access to the non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.
For information about the U.S. Census, see the Census Bureau technical documentation and questionnaires.
You may wish to search Ancestry.com or FamilySearch.org for the U.S. Census and passenger lists. There may be a fee for using Ancestry. Instead, check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
We also suggest that you review NARA’s Resources for Genealogists, as well as the FamilySearch Research wiki for United States Genealogy. In addition, the document Suggestions and Advice for Family History Researchers may be useful.
We hope this is helpful. Best of luck with your family research!