How do movies and TV shows replicate the White House?
House of Cards is a great example. It looks so real, I thought it was actually in the White House.
They use sets.
They build elaborate stages for the actors to work on in a studio and they replicate the actual locations using photos and historical information.
An article in Architectual Digest even addresses the House of Cards set:
Production designer Steve Arnold is behind the look of the Underwood White House on Netflix's House of Cards. While the team was able to tour the building's public spaces, they relied of archival photographs to create the private residences. “You try to get as much of the character’s story as possible into the set,” Arnold told AD. “We thought about what kind of artwork the Underwoods would hang on the walls, because when you become the president you get to choose some of the decorating and artwork. You have access to most of the art in Washington, D.C., in the galleries and museums.”
Considering how many shows and films have used the "White House" there are probably dozens of versions of the set that have potentially even been used in multiple different projects.
There's even a (dated) site that discusses how close to realistic various shows/films have come to actual accuracy in their versions. As an example, here's an excerpt about Independence Day.
The Oval Office replica is great. Paintings look good such as Avenue in the Rain and The President's House, as well as the required Bronco Buster sculpture by Frederic Remington. The couches look to be of the Clinton color scheme and the oval rug looks to be the simple two-tone blue and gold seen during the Nixon years. They even have the patterned hard-wood flooring correct. And the north doors of the Oval Office have the hidden quality of the real thing. We only get a look at one hallway leading to the Oval Office but it seems accurate enough. We also get a glimpse of the Cabinet Room that looks very good and even has the back of the president's chair a few inches taller than the others, just like the real thing.
The only inaccuracies seem to be the Press Briefing Room which doesn't look much like the real thing and is far too big. It seems that if you want a convincing briefing room, you only need to have a blue curtain with a White House logo hanging in the back. And at times the second floor of the residence has too much activity with staffers walking around. You get the impression that some aides are walking into the Master Bedroom to make photocopies. In one of our last looks at the White House we catch a short glimpse of the Diplomatic Reception Room foyer which instead of having the Views of North America wallpaper, the walls are lemon yellow. But it's still a convincing interpretation. Once outside we see that the south portico area of the house exterior looks very accurate.
Some of the examples are also enumerated in a New York Times article by Linda Lee (from 1997) about the various Oval Office sets.
One Oval Office is available from Castle Rock Pictures, which built an extensive White House set -- East Wing and West Wing -- on the Culver lot in Los Angeles for the 1995 film ''The American President.'' The Castle Rock Oval Office has since been used for Disney's ''Nixon'' and 20th Century Fox's ''Independence Day.''
But until recently most productions borrowed the Oval Office that Warner Brothers built for ''Dave,'' its 1993 film about a Presidential impostor. ''It's something that's very distinctive, and a lot of people want it,'' said Gary Credle, president of Warner Brothers studio facilities.
Apparently, even YouTube built two oval office sets!
As the US election season heats up, many YouTube video creators will want to put out political spoofs, commentary, and songs.
So YouTube built two detailed replicas of the White House's Oval Office.
Unveiled August 30, the Oval Office sets live at the LA and Manhattan YouTube Spaces. Any creator with at least 10,000 subscribers can film a video there, YouTube Spaces' Director Liam Collins tells Business Insider.
As to how... the White House is largely open for tours (if you can get a ticket) and there are thousand of photographs of the interior. As you can see in the House of Cards example, they were given a tour of the building. It's pretty easy to know what these rooms look like from the decades of visual materials to go off of.
Consider, also, that the average viewer doesn't know what the actual rooms look like other than these same photographs and videos, so if they're well-depicted in photos they can be very accurate; if they aren't, they don't really need to be.