Emigrant Ship Rosters
There is one source, World-Wide LDS Ship Registers that will provide information concerning which microfilm to look up to find an LDS roster for each voyage. Also included is a U.S. roster (if one exists), that is the one taken at arrival port e.g. New Orleans, New York, Boston, etc. Most voyages began in Liverpool, England, so many had a smaller trip from Germany, Denmark, etc. to get to England and then most traveled by train to Liverpool.
The information from World-Wide LDS Ship Registers has been consolidated into a useful page with a table showing ships and Mormon emigrant companies from 1840 to 1868 with links to pages showing which microfilm to use when looking for a roster.
If you are unsure of the ship or the year of the voyage or the ship name you can search other indexes to find out when your ancestor came across the Atlantic. A good starting point is the European Emigration Card Index. If your ancestor is not listed here then a search of the European Mission Emigration records is required. If still no entry is found and your ancestry came from Scandinavia then take a look at the Emigration from the Scandinavian Mission. It should be stated that many companies traveled together from start to finish, however at the same time a few sometimes stayed in the Midwest for a time or found work elsewhere to save up some money prior to the trek across the Plains, so the year they came across the ocean is not always the year they came to Salt Lake City.
Documenting the Voyage
To better understand how the emigration worked see Andrew Jenson's article on the mode of emigration that details emigration in the 1850's. Another related article, By Sea by Gustive O. Larson is also available. An excellent bibliography is in Mormons on the High Seas that lists ships alphabetically and the year of the voyage along with references to narratives by those who made the trip. If you ancestor came from Scandinavia see the History of the Scandinavian Mission. One great resource that is often overlooked is the Millennial Star. This was an official publication of the British Mission. Many letters were printed in the Millennial Star that were between the company leader and church leaders in Europe. These letters provide some details not available anywhere else.
The article Sailing Vessels and Steamboats provides a brief summary of each emigrant ship's voyage from 1840-1869.
To get a feeling for what the voyage must have been like read Under Sail to Zion by Conway B. Sonne. The article also shows the shapes of the different types of boats.
One interesting thing is that only one ship that carried LDS passengers ever wrecked in the 1840-1890 time period. The Julia Ann is only the ship with that distinction.
Charles Dickens wrote about some Mormons leaving England in the Uncommercial Traveller.
There are two excellent resources that discuss the Mormon migration by sea.
Ships, Saints, and Mariners: A Maritime Enclyclopedia of Mormon Migration, 1830-1890 by Conway B. Sonne; University of Utah Press.
Contains a history of each Mormon emigrant ship. Contains several photographs and many interesting tables at the end of the book.
The book is available at the Salt Lake City Family History center under the call number of US/CAN 873 w2ss (no microfilm is available on this book).
Saints on the Seas: A Maritime History of Mormon Migration by Conway B. Sonne; University of Utah Press
This book contains mostly narratives of voyages. It includes travel by water on the way to the Midwest.
The book is available at the Salt Lake City Family History center under the call number of US/CAN 873 w2so (no microfilm is available on this book).