The Orchestra and the Chorus
The orchestra would be a flat area and might be a circle or other shape with an altar [technical term: thymele] in the center. It was the place where the chorus performed and danced, located in the hollow of a hill. As you can see in one of the (albeit, restored) Greek theater photos, the orchestra could be paved (as with marble) or it could simply be packed dirt. In the Greek theater, the audience did not sit in the orchestra.
Before the introduction of the stage building/tent [technical term to know: skene], entrance into the orchestra was limited to ramps to left and right of the orchestra, known as eisodoi. Individually, on theater drawing plans, you will also see them marked as parados, which can be confusing because it is also the word for the first choral song in a tragedy.
The Skene and the Actors
The orchestra was in front of the auditorium. Behind the orchestra was the skene, if there was one. Didaskalia says the earliest extant tragedy that utilizes the skene was Aeschylus' Oresteia. Before c. 460, actors probably performed on the same level as the chorus -- in the orchestra.
The skene was not originally a permanent building. When it was used, actors, but probably not the chorus, changed costumes and emerged from it through a few doors. Later, the flat-roofed wooden skene provided an elevated performance surface, like the modern stage. The proscenium was the columned wall in front of the skene. When gods spoke, they spoke from the theologion which was on the top of the proscenium
The Theater of Dionysus in Athens, by the Acropolis, is thought to have had 10 wedges, one for each of the 10 tribes, but then the number was increased to 13 by the 4th century. The remains of the original Theater of Dionysus consist of 6 stones excavated by Dörpfeld and thought to be from the orchestra's wall. This is the theater that produced the masterpieces of Greek tragedy by Aeschylus, Sophocles, and Euripides.
Note: For the bibliography, see the previous page.
Photo CC Flickr User seligmanwaite