This is a pretty clear example of the "Call." That's because, literally, a god (Apollo) appears and tells Orestes what he's got to do: go to Athens and pray to the goddess for help. This is echoed by a parallel call, from the ghost of Clytemnestra to the Furies, when she sends them in hot pursuit of our (sort of) valiant hero.
Okay, so we don't actually see Orestes go to Athens, but we do see him arrive there. Assuming that Aeschylus never watched Star Trek, and that teleportation wasn't part of his dramatic repertoire, we think this means Orestes had to make a journey to get there. Remember, this is a play, so some of the plot elements will necessarily have to be compressed or simply implied. The trip from Delphi to Athens is one such element.
Arrival and Frustration
Just when Orestes arrives in Athens and prays to the goddess Athena for help (as Apollo told him to), the Furies show up after him. It looks like he isn't out of hot water yet. This becomes even clearer once the Furies sing their magical "binding song," which anchors him to the spot.
The Final Ordeals
As in your typical episode of Law & Order, the final ordeal of Orestes' quest is a trial. Athena is the judge, the citizens of Athens are the jury, the Furies are the prosecuting attorneys, and Apollo is the defense attorney. Orestes's fate hangs in the balance as the two attorneys conduct cross-examinations and make arguments in an attempt to persuade the judge and jurymen.
Once the jury's votes are cast and Athena breaks their tie in favor of Orestes, our hero is home free. He heads off to Argos in high spirits, pledging to make his city allies with Athens forever. This doesn't leave much for the plot to wrap up, except for the small problem of what to do with the ravenous Furies, who are hell-bent on obtaining Orestes's blood, verdict or no verdict.
When Athens persuades them to become goddesses in favor of helping good people as well as harming evil people (leading to their name-change to the "Kindly Ones" or "Eumenides"), the plot gets all tied up with a nice little bow.