You never know when you'll need the security of a secret underground room. Whether you want a secure place to hide your valuables or take shelter during a tornado, a secret underground room will offer privacy from prying eyes and a safe haven.
Plan to enter your secret underground room from your basement. If you don't have a basement, you can still build one but the access will be less secure.
Excavate the outside soil where you want the room to be. Placement is important because you want to hide the evidence of the room underneath a large porch or a deck. It's tricky to try to cover the roof of the room with soil because it will eventually biodegrade and settle.
Form and pour concrete reinforced walls, using rebar in teh walls and putting conduit in the forms before you pour to allow access to wiring later. Plan for either a ceiling or wall air vent at this time and frame it in.
Pour the floor and install a steel-reinforced ceiling. If you're really worried about someone getting in, you can frame and pour the ceiling, too but as long as you hide it under a deck, it's not that important.
Frame the access from the basement by installing paneling on the entire wall and putting a single piece of paneling on the back of the secret underground room door. Make sure the panel fits well when the door is closed.
Don't get a permit to put in the room. This might be a sticking point for you. In some rural areas, permits are not required but in many places you must have one. As long as you have a tall fence and tell your neighbors you're just installing a patio and a new deck, they may not notice.
Keep the secret of the underground room until after you sell the home. Then go back and inform the new residents of their "bonus" room.