Exposition provides the who's who and the what's what of any given story. It's the part of the plot that sets up what the story is about and helps us get to know the characters. In The Left Hand of Darkness, that's basically chapters 1 to 5.
During these chapters, we get to know Genly Ai, his mission, and his predicament. His mission: to convince the Gethenians to join the Ekumen. His predicament: the Gethenians are androgynous aliens, so he has a hard time navigating their social circles and political games.
In short, the man is nowhere near equipped to deal with the situation at hand.
And then there's Estraven, a mysterious Gethenian who may or may not be trying to assist Ai in his mission. Neither Ai nor the reader can tell what Estraven's about because his words are akin to a mental Rubik's cubes—it's (almost) impossible to straighten them out.
During the Rising Action, things get complicated but in a good way (good for the reader, anyway). The protagonist has to deal with new obstacles to meet his goal and encounters new characters who may be trying to help or hinder him.
In The Left Hand of Darkness, the new complication is Orgoreyn. Here, Ai has to learn to navigate a new Gethenian society after having just failed to navigate Karhide's culture. The Orgoreyn Commensals also complicate the plot because some are trying to help Ai with his mission but others are trying to bury the knife pretty deep in the man's back. If Ai can't tell friend from foe, his mission in Orgoreyn will fail.
Also, the Ai/Estraven relationship grows more complicated. On the one hand, the reader now knows Estraven is trying to help Ai but can't communicate his purpose to the man. On the other hand, Ai still has no idea what Estraven's trying to accomplish, leading to what your English professor would call "dramatic irony."
The rising action runs roughly from Chapter 6 to Chapter 12.
The Climax marks the point of no return, the event horizon; all bets are in, there's no going back…you get the idea.
When the Commensals of Orgoreyn betray Ai Caesar-style, the climax begins. Ai's mission is now close to critical failure as he enters the Volunteer Farm. There, he is forced to work in the extreme Gethen weather and is drugged and tortured to near death.
So, you might hear "Falling Action" and think that things are about to settle down. Nope. Often, the Falling Action contains some of the most exciting moments in a story. Those in the biz of story analysis call the stage Falling Action because the story's conflicts wind down toward conclusion—but often in really exciting ways.
In The Left Hand of Darkness, Ai and Estraven's journey across the Gorbin Glacier—a.k.a. the Ice—represents the falling action (Chapters 15 to 19). Here, some of the conflicts set up during the exposition begin to resolve. Estraven and Ai finally see eye to Ai (get it?). Their conflict of miscommunication slowly breaks down and is replaced with friendship. Likewise, Ai begins to understand Gethenian culture as its own thing and not just from his Earthian perspective.
Of course, there's still one last conflict that needs wrapping up: Ai's mission for the Ekumen.
And that's what the resolution is for. Resolution provides closure for all the nagging plot threads and conflicts of the story—well, it should at any rate.
When Ai contacts the Ekumen, his mission is complete. King Argaven's hand has been forced, and he can no longer ignore the reality of the larger universe. With Obsle and his allies taking over the Commensals of Orgoreyn, the same might be said of their country. Also, Tibe resigns from his position, effectively ending the threat of war. The Ekumen ship arrives, and it's time to ride off into the sunset, and….
But wait, what about Estraven? He was branded a traitor for what he did; doesn't he get resolution?
Yes and no. Officially, Estraven is still considered a traitor by the story's end. King Argaven just won't repeal the status. But Ai is able to tell the story to Estraven's father and son. So, while Ai's friend may still be considered a traitor, at least there will be those who know being a traitor to one country means not being a traitor to mankind. Not a bad resolution for him, in our humble opinion.