There are many doors in the game. Simply open a door, and then use the close action icon on the open door to close it.
*** Spoiler - click to reveal ***Usually that achievement unlocks during the regular progress of the game when you close the door inside the room with the sleeping conventioneer to get his keys from the door that looks like the door in the achievement icon.
In this room you also get
This only works on doors that stay open, not on the swinging door for example in the back of the Founding Fathers Room.