[Excerpted from http://lilt.ilstu.edu/drjclassics/lectures/theater/ancient_greek_theater.shtm]
The Orchestra: Even the most primitive of Greek theaters had the most important of these elements: the orchestra, or "dancing-place." It was in this circular area that the chorus, a group of 12-15 actors in a single unit, sang and danced. In the archaic Theater of Dionysus in Athens (left), the original orchestra floor was just smoothed dirt and was eventually replaced with polished stone as the architecture of theater evolved. In the center of the orchestra there was an altar to the god Dionysus where a flute player was stationed.
The Theatron: Classical theater is all about spectacle. In Greek, theaomai means "to view" and theatai were the people who viewed the performance, or the "spectators" in a theatron, or "viewing area." Roman "auditorium," conversely, comes from the Latin word audio, "to hear." Everyone in the Greek theater was assured a clear view of the orchestra and the stage (there were no support pillars that could block one's view) and since the theater is built into an already existing hill, the seats are naturally arranged on an upward slope, assuring that each tier of seats is above the next. But even though the designing focus was on a good viewing area, the Greek theater boasts magical acoustic properties as well. A single individual's voice—or even the sound of a match being struck—rises clearly to the uppermost seats, unless it is overpowered by a raucous chorus of competing crickets.
The Skene: One of the first modifications to the basic performance area of archaic theaters was the addition of a portable wooden stage area, which was later replaced with a more permanent design. By the time of Aeschylus, the skene came complete with a painted (probably) facade representing the power source of the play, usually a palace or temple. The backdrop also included a door, through which actors could enter and exit the performance area. Murders and other violent scenes were usually performed out of sight of the audience, "behind closed doors." Therefore, classical theater often resorted to the use of a wheeled cart called an ekkyklema to divulge the activity acted out "behind the scenes." The most typical burdens of the ekkyklema was the corpse of a murdered individual.
The Parados: The circular pathway that surrounds the orchestra is called the parodos and can be accessed from either side of the skene. The parodos is an important element of the Greek theater and serves a double purpose: first, it provides the audience with a way to access their seats. More importantly for the purpose of staging the play, though, it provides access to the chorus and some actors to the orchestra. The chorus never entered the orchestra from the skene, and some characters are denied access because they lack the might and right to be associated with the power structure represented by the skene: messengers, visitors, exiles, etc (see mini-lecture below for an example of staging a Greek play). It is not uncommon, however, for characters to move freely between the skene and the orchestra. In the case of human beings, ramps or stairways serve their purpose, but in the case of divine messengers or visitors, a mechane (crane) would lift them bodily into the air. Eisodoi are the ramps that give access to the paradoi, and the Romans were particularly fond of creating elaborate stage areas.
The orchestra was the chorus's domain; actors generally remained on the skene unless they entered the performance area through a parodos directly onto the orchestra.