Betsy Larsen (Larsen) estimated 1855 birth date

[Charles Henley]

I am an American search for family information and personal information regarding Betsy Larsen or Larson who was born in the Varmland area in the 1850s and migrated to the USA around 1870.  Eventually she married John Bergquest (formerly Johannes Jonson who came from Smaland).  I know nothing else about Betsy except that she was poor and migrated to the United States by herself.  
 
Please help me with any facts or advice in researching my Swedish relatives.
 
Charles Henley
New York City