Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Initial Situation
Eddie is a little overprotective of Catherine. Beatrice's illegal immigrant cousins arrive from Sicily.
All seems well in the Carbone household. Eddie isn't particularly happy about his niece, Catherine, getting a job. He chills out about it, though. All it takes is some big doe eyes from Catherine and some tough talk from Beatrice, his wife. We also meet Beatrice's Sicilian cousins, Marco and Rodolpho. The illegal immigrants are going to hang out at the Carbone place until they can find their own crib. Marco is here is to send money home to his starving, tuberculosis-ridden family, and Rodolpho is here to stay. Eddie immediately warms up to the Marco but is suspicious of the singing, sewing Rodolpho. Uh oh – all the pieces are in place for disaster.
Conflict
Eddie swears to stop Catherine from fraternizing with Rodolpho.
Catherine and Rodolpho are late coming home after a movie. Eddie is out in the street, pacing and freaking out. Apparently Catherine and Rodolpho have been out quite a bit lately, seeing the beautiful sights of their lovely little slum, Red Hook. Beatrice fails miserably at calming Eddie down about the situation. Eddie goes on and on about how unmanly Rodolpho is. Apparently, men who sing and have blond hair just "ain't right" in Eddie's book. The main conflict becomes pretty clear when Eddie swears to put an end to the budding romance.
Complication
Eddie goes to the lawyer, Alfieri.
Eddie tries every argument he can think to convince Catherine that Rodolpho is no good: He's not a working man! He's just wants to marry you to become an American! When Catherine doesn't buy it, Eddie takes his first solid action in the play and meets with a lawyer, Alfieri. He hopes that there's something the law can do to stop the relationship. There isn't.
Climax
Eddie forces a kiss on Catherine and Rodolpho.
Eddie comes home drunk and finds Catherine and Rodolpho exiting the bedroom. As you might imagine, he goes absolutely nuts. As you might not have imagined this insanity manifests itself in a bizarre double kiss. He forces his lips on Catherine and does the same thing to her boyfriend. Talk about an explosion of emotion.
Suspense
Eddie turns in the immigrants.
Things get suspenseful when Eddie calls Immigration on Rodolpho and Marco. We're on the edge of our seats. Immigration storms the building and arrests Marco and Rodolpho. Marco spits in Eddie's face and calls Eddie out in front of the whole neighborhood. Everybody thinks Eddie is villain.
Denouement
Marco and Eddie duke it out. Eddie dies by his own knife.
Marco shows up, fresh out of the prison cell that Eddie sent him to, and basically challenges Eddie to a duel. Eddie pulls a knife. Marco drives it into Eddie's chest. There you go. Game over. When your protagonist gets killed, the action kind of has to be resolved.
Conclusion
Alfieri sums it all up with a lovely little monologue.
Miller concludes the play with speech by Alfieri. Read it carefully. If you didn't pick on the major themes of the play along the way, Miller pretty much tells you what it all meant.