This paper gives basic information necessary to run X-13ARIMA-SEATS, and it shows examples for setting up input specification files (spec files) and how to use Win X-13, the Windows interface to X-13ARIMA-SEATS.
This paper shows some examples of using X-12-ARIMA, starting at the beginning and following all the steps, including use of graphs.
These are the Census Bureau guidelines for using seasonal adjustment diagnostics available from X-12-ARIMA.
This manual is not the kind of thing you'd sit and read from front to back, but when you're running X-13ARIMA-SEATS, it is very helpful to have this handy so you can look up specific details about the input specifications. There are introductory chapters that have good information about time series.
Not everything in this paper is for the person starting out with seasonal adjustment, but it covers a lot of ground, so this is a good paper to skim.
This is quite long, but it has a great deal of information about the seasonal adjustment procedure of X-12-ARIMA and about the diagnostics.