Between 1820 and 1920, 35 million immigrants arrived in the USA, the majority of them at the port of New York. To search for an existing list you need to know your ancestor's name, approximate date of arrival, approximate age at arrival and port of arrival.
If your ancestor arrived after 1819, he may be listed in any of the following
Customs Passenger lists begin in 1820. A passenger list will usually provide you with name, age, sex, occupation, country of origin, port of departure, destination, date of arrival and name of the ship.
Immigration Lists (Ships' Manifests) after 1883 give more detailed information.
The National Archives has the customs and immigration passenger lists and indexes from 1820 to the 1950s. You can request a search of the records at the National Archives http://www.nara.gov/ with form NATF 81. You must submit one form each person or family group traveling together. You can obtain the NATF Form 81 by providing your name and mailing address to firstname.lastname@example.org. Specify "Form 81" and the number of forms you need.
The Family History Library in Salt Lake City has microfilmed copies of passenger arrival records and indexes from the National Archives. If you find your ancestors in any of the indexes you should then consult the original passenger lists.
Indexes for which are microfilmed and available through your local FHC are:
1820-1846 FHL computer number 15681
1897-1902 FHL computer number 92040
1902-1943 FHL computer number 92040
1848-1891 FHL computer number 217426
1899-1940 FHL computer number 92077
1820-1897 FHL computer number 218234
1897-1952 FHL computer number 175219
1833-1866 FHL computer number 175226
1800-1906 FHL computer number 216604
1883-1948 FHL computer number 175209
1853-1952 FHL computer number 216594
Lists and indexes for Charleston, Galveston, Key West, New Bedford, Passamaquoddy, Portland Maine, Providence, San Francisco, Seattle, and other ports can be found at the Family History Library and the National Archives.
There are also CD-Roms that index arrivals 1820-1850. See the list of CDs on the right hand navigation bar of http://olivetreegenealogy.com/ships/
There are various hard copies (books) of indexes and lists, and I will discuss those at another time. There is also the online Ellis Island Database 1892-1924. The best way to search it is through the One-Step Search Engines at http://stevemorse.org/
There are many online lists and to start your Internet search for ships' passenger lists, begin at The Olive Tree Genealogy Ships Section
Ships to USA start at Index to USA Ships Once on this page you can choose by state, or by year of arrival.