Well, moving a working locomotive is relatively easy compared to a non-working one ;-)

IIRC, the way they did it was to hook onto the local rail line; probably just long enough to get the train onto the "spur" - then move the tracks back.

Doing that just takes a lot of people and labor (you've probably seen old films of track laying from the late 1800s-early 1900s).

They wouldn't install a switch, as that would be too costly for something so temporary; so they probably just broke the track, moved it sideways a bit, connected it to the new "spur", moved the trains/cars onto it, then reconnected it back to the original line to allow traffic thru. Then basically the reverse to move in equipment to dismantle/haul away the remains.