As you attempt to determine when your family might have come to the United States, you can use timelines and such to determine a basic time period that one of your family's ethnic group immigrated.
For example, there were a lot of German's who immigrated to the United States between 1820 and 1860.
You need to know a time frame for when your family's ethnic group came to the United States, but you do not need to know the exact date. An estimate such as 1820-1860 is appropriate.
Below are some resources that try to do just that.
Once you have a basic idea of when your family possibly immigrated to the United States, you need to find out more about what the immigrant experience was like as immigrants tried to assimilate to their new country.
Assimilate: to absorb into the cultural tradition of a population or group (Merriam-Webster Dictionary)
In other words, what would your family have had to do to try to fit into their new country and what might they have experienced while trying to do so.
A great web resource that contains history and information of a variety of ethnic and racial groups that migrated to America includes Multicultural America.
Below are a limited number of other websites that may help. This is not an exhaustive list, so you should also do some Googling yourself. If you Google something like "Irish American immigration to America" (or migration to America) you will likely find something useful.
DO NOT USE WIKIPEDIA AS A SOURCE FOR YOUR PAPER!
Warren County Community College
Haytaian & Maier Library
475 Route 57 West
Washington, New Jersey 07882