We are flying from Vancouver YVR to Amsterdam AMS and onto Budapest BUD with KLM. Do we go through customs in AMS or just transit the airport?
As the flight Amsterdam to Budapest is a within Schengen, you go through immigration and passport control in Schiphol, Amsterdam airport.
You will only go through customs when you leave the flight area of the airport, you will go through customs (the green and red channels where you declare what you have brought if you have something) in Budapest.
As a transit passenger who does not need to pick up luggage and check it in anew, you will not leave the flight area of Schiphol, Amsterdam Airport. The airport is basically divided in a few terminals but they are connected both sides of the security walls and you can always walk from one part to the other.
So you would not go through customs in the Netherlands, you do that when you arrive in Hungary.