Identify the immigrant. Look at his or her name, given and surnames are important. Is there a known middle name? Germans usually had two or three names preceding their surname, such as Johannes Michael or Johannes Adam Georg. What name did they use? Normally they would use one of the middle names, such as Michael or Adam or Georg. The same family may have several Johannes' along with John and Johann. Female children may be no different, such as Maria Anna and Maria Gertrude and Maria Dorothea. Once again, look at the middle name. However, keep in mind that there are several given names as a possibility. As for surnames, make a chart showing any changes the name underwent in spelling. These could be changes made within the family or changes you have noticed in records here in the United States, such as in census, deeds, etc.
What dates accompany your immigrant? While it is preferable to have a nice full set of dates, that is often impossible. Your research may have only provided an approximate date, such as from census. Make sure you identify the source of these dates. They are a working point in the right direction.
Where are they when? Forget the fact that you are wanting to know where they lived in Europe or another foreign area. Where are they when you found them here in the United States? Identify all places you have found them, such as on deeds, in probate records, tombstones in the cemetery, newspaper articles, census, etc. Where can you look to fill in the gaps? What records are available that you have not consulted?
Naturally you are seeking to know more than they came from Germany. To do any type of research in a foreign country you must know the exact area where they lived. That means a parish or town, province and any other jurisdiction pertaining to the particular country. Keep in mind that boundaries changed in foreign countries just like the counties did in our states. Would you started looking for your ancestor, John Jones, who was born in United States in 1840 and hope to find him. If you have no clue as to the state and/or county, the task will be unbearable. To locate that exact place in the foreign country, you must seek out records created in the United States that contain clues. These can be anything from a slight mention in a newspaper article of a location to naturalization papers to death certificates. Keep in mind that many kept their religious affiliations here that they had in the old country. The church may have kept more meticulous records than you realize.
The technique doesn't work for your immediate ancestor, may work for a relative. If you can't find a death certificate for your ancestor, you might consider looking for one of a sibling. Some research I did a few years ago produced no death certificates with place of birth for about five children and finally one death certificate showed the exact village in Germany where she was born. Once I ordered microfilm of parish registers for that village through my Family History Center, I found the rest of the children, including the ancestor.
Look at the people who surrounded your ancestor. Were they from the same foreign country? What was the "draw" to the area? Did they all know each other or come to the United States at approximately the same time? True, you don't want to research a total stranger's ancestry, but sometimes a look into their background will provide just the clue you need.
Once you have all of this information in front of you, begin looking at passenger lists. There are many available now on Internet, one of the largest collections being at Ancestry.com. Don't forget the large collection of passports at the same web site. Many people returned to their former country of origin to visit. Take advantage of everything available on Internet. Are there other people researching your immigrant? What information do they have? How well documented is the information?
It's not easy to jump the pond, but it can be done. Sometimes it takes a long time, but the road will be interesting, particularly if you keep track of what you are doing