How they came here: Immigration & Naturalization
Immigration Records
Ancestry Library Edition contains New York Passenger Lists, 1820-1957 with links to original images, and numerous other immigration record sets.
The National Archives has several ethnic passenger lists available online.
Passenger and immigration lists index: a guide to published arrival records of about 500,000 passengers who came to the United States and Canada in the seventeenth, eighteenth, and nineteenth centuries, ed. by P. William Filby, with Mary K. Meyer. Detroit, Mich: Gale Research Co., 1981. 3 v. The standard printed index. Given the problem of spelling variants, it may be worthwhile to browse this when a name does not turn up in Ancestry.
Naturalization Records
Naturalization Records are kept locally so may be difficult to find. Local indexes and documents on microfilm or occasionally digitized exist and may be found via Ancestry Library Edition, WorldCat (the proper subject term is Naturalization records), USGenWeb Project, RootsWeb and FamilySearch.
National Archives - Naturalization Records: Introduction and Links to Resources
Reference Books
Guide to naturalization records of the United States, by Christina K. Schaefer. Baltimore, MD: Genealogical Pub. Co., 1997, 394 p.
They became Americans: finding naturalization records and ethnic origins, by Loretto Dennis Szucs. Salt Lake City, UT: Ancestry, 1998, 294 p.
American passenger arrival records: a guide to the records of immigrants arriving at American ports by sail and steam, by Michael Tepper. New ed. Baltimore: Genealogical Pub. Co., 1993, 142 p.