Back when the settlers used to load up their covererd wagons and head west to california, how long would the trip by wagon typically take?
It depends on where you started and where you wanted to end but in general a wagon trip took about three months from the central plains to the Pacific.
And routes to the West improved throughout the century so someone heading out in 1801 probably was at a distinct disadvantage compared to someone leaving in the 1890’s.
I would think taking a steamer or sailing ship would have been faster than going by wagon (no cite).
Of course once the railroads were built the number of people heading out on wagons would have dropped off considerably.
By 1860 you could take a steamship from New York to Panama, a train across Panama, and a steamship from Panama up to San Francisco, in about 3 weeks.
For a cite, see this book, Up and Down California, by Stephen Brewer. New York to San Francisco, from October 22 to November 14, 1860.