It is extremely difficult to read this play without thinking of the middle portion of Aeschylus' trilogy, and this is doubtless Sophocles' intention. Thus, try always to keep in mind general questions such as:
What has Electra's life been like?
Is she a sympathetic character? Track the Chorus' attittude through the action.
What effect does making Electra more central to the action have on the play?
If you have read Antigone, compare the relationship of the two sisters in each play.
Pelops, Orestes' great-grandfather is mentioned in this play several times (e.g. 501), but not in Aeschylus. Why is his story significant? Look it up at the Perseus site.
Is Clytemnestra more or less sympathetic here than in Aeschylus? Is she different in any fundamental way?
Note the difference in Electra's account (565ff) of the reasons for Iphigenia's sacrifice.
Why do you think the false story of Orestes' death is so much more elaborate here than in Aeschylus? For one suggestion, read this on-line essay.
Note how much more difficulty this Orestes and Electra have recognizing each other. And how their rejoicing almost blows his cover.
The translation often refers, awkwardly to a "Genius", and this is a loose translation of the Greek word daimon, which suggests spirit or supernatural being.
How does Sophocles' reversal of the sequence of the murders change the story, if at all?
Is Electra really better off at the end of the play than the beginning?