It is not possible to tell from your Family Finder results if a match is from your mother’s side or your father’s side. This is because autosomal DNA recombines each generation. With an autosomal genetic test, the only sure way for you to tell if your relationship with a match is on one parent’s side is to test that parent.
To find the genealogical connection with your match, you need to consult traditional genealogy records. These are birth, marriage, and death records. They also include documents like the census.