The best place to start is the U.S. Census, which contains numerous clues about an ancestor's place of origin.
Another excellent source for discovering a place of origin are vital records, which recorded major life events.
Marriage and death records for an ancestor and/or other family members (including siblings who may have accompanied an ancestor across the ocean) may list birthplace information.
Birth records for children of the ancestor born in the United States may contain similar information. Many indices are available to help in the search for these records.
Historical newspapers from an ancestor's residence in the U.S. are a source not to be overlooked. In addition to providing the context of life in that locality, newspapers may also hold precious clues to a German place of origin.
Obituaries, birth and marriage announcements, and news articles are among the multitude of sources to check in the newspaper.
Also consult U.S. passenger lists, naturalization records, and other emigration/immigration records to determine an ancestor's home in Germany. Passenger lists for U.S. ports of arrival often enumerated each passenger with information on his or her place of origin and destination in America.
Naturalization records (especially those filed after 1906) contain important genealogical information, including a renouncing of citizenship from a specific locality in Germany. Naturalization indices are available in book form as well as online.
By assembling the clues found on a myriad of records, you can determine an ancestor's place of origin and then start searching records in Germany.
Q: Is there anyone with this family name left in the United States, and where did it originate from? -- Pyska, Westland, Mich.
A: Yes, even focusing on just this exact spelling, the name Pyska is found in New York, Michigan, Maine, Rhode Island, Illinois and Pennsylvania. Try searching on just this surname at www.ancestry.com.
You'll find hits in various census, immigration, WWI and WWII draft registration records, as well as the Social Security Death Index and a few other resources. There are also 11 family trees that contain the Pyska name, so if you're lucky, one of your distant cousins is already researching your family.
Unfortunately, it's hard to pin down an exact location of origin. A check of the immigration and WWI draft registration reveals a handful of locations -- Sokolow, Lubasz, Rutaje and others -- so it's hard to say where a given family might be from without knowing specifics. But the majority seem to hail from the region known as Galicia, often noted in records as Poland or Russia.
Q: My maiden name is Piper. My father's name in Milton Milo Piper. His father's name was Milo Piper. I have no idea as to where my paternal ancestry traces back to. Both my father and grandfather were from Muskegon, Mich., but that is as far back I can find. -- Patty Dahlman, Grand Haven, Mich.
A: I took a peek at some census and other records on Ancestry.com and see that your grandmother was widowed young. Your father makes an appearance in the 1920 census as a toddler living with his mother and maternal grandparents in Muskegon.
From your grandfather's WWI draft registration, though, I can tell that he was still alive in September 1918. So he must have died between then and January 1920 -- flu? WWI?