First of all it's the language. If you don't know the language you don't know how to find them. And you can't read any records.
Geography is another thing. If you find your ancestor coming in to Galesburg in 1880, departed from Gothenburg, it is quite impossibe to tell where he or she really came from. The port of departure was seldom the place of origin.
Name change and use of name; if they were born before 1890 they most probably were born with a last name taken from their father's first name, also called a patronymic, or patronym. It is a component of the last name based on the name of the fathers' first name. In many areas patronymics predate the use of 'family names'. For example, the son and daughter of Peter Magnusson would have different last names - Petersson (for his son) and Petersdotter (for his daughter). Son of Peter or daughter of Peter.
Patronymics can simplify or complicate the research! Why?Migration has frequently resulted in a switch from a patronymic to a 'family name' (normally the father's last name) due to different customs. Most immigrants "adapted" to the new customs as soon as birth, marriage, and death certificates had to be written down by someone else. So, your Nels Nelson born in Sweden in 1855 was most probably born with a different last name. Unless you know more about him and his father and his past, his origins, it's going to be difficult to trace him.
A Bengta Sonesdotter became Betty Munson or Monson as she entered the US if she was married to a Nils Månsson. As soon as she entered the US her name could have changed. And the women could not keep their maiden names which was the tradition in the Old World. You don't find any maiden names in the US census unless the woman is single. They all get their husbands family name. So it can be really hard to find someone back in Sweden if you don't know the original name. You may find your female in the emigrant records, with her maiden name, that's easy, but as soon as she reaches a US port it may be a different one.
Read more about name changes and 'tricky' cases in my Special finds section.