ETA - Not sure what happened to the formatting as it was fine in my browser. Sorry about that. And sorry about the delay in cutting it - different time zones!
The Transcontinental route was created in 1869 when the Central Pacific Railroad and the Union Pacific Railroad tracks were joined at Promontory (near Ogden, Utah), opening up a single route from East to West Coast that took 7 days continuous travel from NY or Boston. In brief, anyone travelling from say New York or Boston would go as follows:
New York (actually New Jersey) or Boston to Chicago on the New York Central and Hudson Valley Railroad ( Day 1 and 2)
Chicago to Omaha by one of three possible lines, but the Chicago, Rock Island and Pacific Railroad would do nicely. (Day 3)
Omaha to Council Bluffs/Ogden (Utah) by the Union Pacific Railroad (Days 4 and 5)
Ogden to Sacramento by the Central Pacific Railroad (Days 6 and 7 – noon)
Sacramento to San Francisco (afternoon and evening, Day 7)
History of the Railroads in the US - http://mikes.railhistory.railfan.net/
The Central Pacific Railroad Museum site is an absolute treasure trove and a gem. It has hundreds of historical documents online that would make any researcher swoon – far too many to list here.
This page - http://cprr.org/Museum/index.html#Read – has a massive list of links on dozens of different aspects of the railroad. Go down the page until you get to the yellow section (the colours on the website are unfortunate) and start browsing through the hundreds of documents and links. Some highlights:
The First Transcontinental Railroad by Elizabeth Gibson http://www.suite101.com/article.cfm/old_west/27482
When Railroads Were New by C Carter http://cprr.org/Museum/When_RRs_Were_New.html
Harper's Monthly Magazine article by Charles Nordhoff
Susan Coolidge (of What Katy Did fame) "A Few Hints on the California Journey." by Susan Coolidge, Scribner's Monthly, May, 1873.
Helen Jackson "Bits of Travel at Home." 1887.
Maps and Guides
"Crofutt's Trans-Continental Tourist's Guide." by George A. Crofutt, 1872. (a gem)
"The Atlantic to the Pacific: What to See, and How to See It." by John Erastus Lester, 1873.
"Nelsons' Pictorial Guide-Books: Central Pacific Railroad." 1871.
The Union Pacific Railroad: A Trip Across the North American Continent from Omaha to Ogden." Nelson's Pictorial Guide-Books, 1871.33
"Travelers' Official Railway Guide for the United States and Canada. June, 1870."
Every railroad is listed here with full timetables. Essential resource.