My mom used to tell her school friends that she was related to the actor, Roy Rogers. She wasn’t. As a kid I used to tell people I was half German, half English, half Irish, and half American. Knowing these two things, you could extrapolate that my family tree contains liars and people that can’t do fractions. 
On my dad’s side, it was believed that my first ancestor in America was born in Germany, because he spoke German. Some relatives said he came to America with a brother and that they were from Frankfurt, Germany. However, these details turned out to be incorrect. Within a short generational span, no one in the family spoke German and the family history was lost.
My sister, Paula, the “Nancy Drew” of the family, decided to do some research because she was interested in the details of our ancestry. When she told me she wanted to check into this, I suggested she start with the USA.gov Family History and Genealogy page. It is a great
launch point with all kinds of links to other resources.
She then went to the National Archives website. The National Archives has a terrific Genealogists/Family Historian web section. They have guidance on how to start your family history search, search-able databases, publications, and a list of independent researchers you can hire to help you with family history search.
U.S.
Citizenship and Immigration Services website. You can make requests for USCIS to search its historical indices for file citations related to particular individual. From that information you can request copies of specific records. Check the site for the fees for index searches and copies of documents.
If you are of Native American ancestry, you may want to go to the Department of Interior to trace your Indian ancestry. They have guidance on determining if you are eligible for tribal membership.
Although my sister was able to obtain additional information about my great-grandfather, it was only dates and locations. She didn’t learn what motivated my great-grandfather to leave Prussia, why he chose to settle in Iowa, how he felt passing through Ellis Island, or what his circumstances were as an immigrant. Those are the types of details that can only be learned through the intimate sharing of family stories. While you are conducting your search into the past, don’t forget to pass on your family stories and share your history with your children.