(A public-transport and budget-travel enthusiast's guide to international travel.)
Why?: Flights to/from Seattle-Tacoma are usually cheaper than those to/from Vancouver. The train journeys Vancouver ⇔ Seattle-Tacoma take about 5 hours one-way and are not too bad.
Top level itinerary: Somewhere in Vancouver ⇒ Pacific Central Station, Vancouver ⇒ King Street Station, Seattle ═walk⇒ Int'l District/Chinatown Metro Station, Seattle ⇒ Seattle-Tacoma Intl. Airport.
Travel date: December 2022.
Papers needed: Passport, Visa/eTA for Canada, Visa/ESTA for USA.
Rough budget: US$40 one way Pacific Central Station, Vancouver ⇒ King Street Station with Amtrak + US$3 Metro Int'l District/Chinatown Station ⇒ Seattle-Tacoma Airport.
Getting to Pacific Central Station: The closest station to Pacific Central Station via TransLink (Vancouver's metro train) is Main Street-Science World. However, there is no direct walking connection between the TransLink station and Pacific Central Station. One has to get out of Main Street-Science World station, cross the Main Street and walk about 200 meters to Pacific Central Station, which has to be taken into consideration when travelling with check-in luggage.
At the Pacific Central Station: It's best to be about 1.5 hours ahead of the travel time. There's usually a long-ish queue and passport + customs pre-clearance before boarding. You will drag your check-in luggage with you throughout.
Luggage check-in option for the train only: Amtrak offers a luggage check-in for train passengers, who can leave the luggage at Pacific Central Station and collect it at King Street Station. This is optional; one can also carry their check-in luggage with them and place them in the ample luggage space in each train compartment. I checked in my luggage and received it problem-free at King Street station on a carousel similar to airports, for which the wait time was about 10 mins.
In the train + border crossing: Seats are very comfortable and US American co-passengers, if you have one, being the friendly lot, will keep you very good company if you're up for it. At Peace Arch, border guards will get in and check your passport. This is painless. However, note that the on-board restaurant will stop serving around 30 mins prior to border crossing and will continue only after the border crossing. The on-board restaurant choices are limited and the food is just okay.
Getting off at King Street Station: If you have checked-in your luggage for the train, you'll receive it back at the station on the carousel. King Street station is in the middle of "nowhere." (see Uber note below).
Getting to the Seattle Metro Station: The closest metro station to King Street Station is Int'l District/Chinatown. Take either (a) the stairs or (b) the lift to St Jackson St and take the turn into 5th Avenue, see Google Maps for alternative routes, especially the one where you can cross the 4th Ave and get to the back entrance of Int'l District/Chinatown. Either way it's a 200 meters walk.
Tickets + Getting to Seattle-Tacoma Airport: Tickets (to SeaTac/Airport Station direction Angle Lake) can be bought at automatic vending machines for US$3, which can be paid via Credit Card. I did not explore online tickets, although this was indicated as a possibility. Do not expect the best cleanliness and facilities at the station or within the metro trains, however, they are, however, functional. I travelled at around 10 pm; there were about 2 co-passengers in the compartment, one of which was moaning loudly all through! I did not feel unsafe only slightly irked.
Getting off the SeaTac/Airport Station: Getting off the metro and going to the terminals is very straightforward and is a 100 meter walk. One just needs to follow the signs.
Note: Uber-estimated "nominal" fare from King Street Station to Seattle Tacoma Airport is about US$40-50. The fare varies considerably depending on the demand.