Troilus wants to hook up with Cressida, not fight in some dumb war that's been dragging on for the last seven years. Problem is, Cressida's been playing hard to get. Meanwhile, the Greeks wish their best warrior (Achilles) would come out of his tent and fight, but Achilles is playing hard to get, too. Basically, in the exposition, Shakespeare sets up and develops two separate plots (a love plot and a war plot). Confused? Don't worry—that's what the rising action is for.
Cressida is traded to the Greeks and betrays Troilus with a dude named Diomedes. Also, Hector kills Achilles' lover/ bestie, which really irks Achilles. Meanwhile, Troilus battles Diomedes but, uh, nothing really happens. Now we're all ready to see what happens when Achilles storms out of his tent for the big climax.
Troilus' battle with Diomedes may have been anti-climactic, but Shakespeare finds a good substitute when Achilles and his gang of Myrmidons mow down Hector. Our hero is slain: definitely a climax.
A guy like Hector deserves some props but Achilles is totally disrespectful when he has the dude's corpse tied to a horse so it can be dragged through the dirt. Now we're seeing the effects of all the upsetting climax: dishonor, dishonor, and more dishonor. We're not exactly expecting a happy resolution.
Now that their best soldier and military leader is dead, Troy isn't looking so good. Bummer, right? Well, Shakespeare can't just leave well enough alone. In the last lines, Pandarus tells the audience that he hopes we all get an STD and die. Gee. Thanks. Way to wrap it up, guys.