A atrium house in Pompeii. Notice the impluvium, cistern head (on the left) and fountain in the background. The tablinium is the small area right in front of the fountain, allowing strangers who were passing by to see the Pater familias (family head) on his seat in front of it, a common way to enchant the view in.
Casa del Menandro (Pompeii), the atrium from the inside. Notice the impluvium and compluvium. You may also see the small drain leading rainwater from the impluvium into a cistern. We can also see a household shrine to the left.
You may have noticed the room right ahead in the first picture. This is the famous atrium that the house type is named after. This room is with no doubt the focus of the entire household. This were where clients saluted their patrons (who would sit in the tablinium, originally the masters bedroom, later a sort of working area/archive) and notice on the plan how all other rooms turn to it.
There are a few characteristics that you may look for when identifying this area. It is to begin with, one of, or the, largest rooms in the house and it is all but always situated right after the entrance. You may also notice a small pond (called impluvium) in the middle of the floor and a hole in the room (which is sloping inwards) called compluvium. There are other type of roofs as well, the ancient architect Vitruvius discuss them in his work De Architectura. This is also one of the absolutely best decorated rooms in most roman upper class houses from this time.