For the most part, The Left Hand of Darkness has a First-Person Central Narrator and said narrator is Genly Ai (we'll get to the not-so-most part in a sec). This means Ai is telling his personal story. Let's take a look at a quick example:
I almost let go the sledge-bar to go look for [Estraven]. It was pure luck that I did not. I held on, while I stared stupidly about for him, and so I saw the lip of the crevasse. (19.3)
Notice how the narrator is speaking in the "I" voice. We know what he sees and what he feels, and we can tell it's a central narrator because Ai is central to the action. He travels the Ice, he holds the sledge, and if he lets go, Estraven will plummet to a pretty, if unwelcome, death.
But things get tricky quick. Some chapters are not told by Ai, and some take on different narrative voices. For example, Chapters 6, 11, and 14 come from Estraven's journal. They too are told in first-person central narrative, but the person telling the story is Estraven, not Ai. Same with Chapter 7, only it's the Investigator, not Estraven or Ai speaking.
Chapter 4 is a Karhidish story told in third-person omniscient. Take a look:
It was not the answer Herbor had hoped, but it was the answer he got, and having a patient heart he went home to Charuthe with it. (4.17)
Clearly, someone other than Herbor is telling this story since the narrator uses "he" (the third-person tell) and not "I" (your first-person give away). But even though the narrator isn't Herbor, he still has access to Herbor's emotions and thoughts. Notice how Herbor didn't say it wasn't the answer he wanted, but the narrator knew anyway. So, we call this third-person omniscient narration. In other words, the narrator knows all and sees all. Same goes for chapters 9, 12, and 17.
Whew, glad that's over. Well, almost. To wrap this up, let's consider the fact that Ai has put all these stories together. He may not have written or told them all, but they are all found his report. So, remember when reading that while some of these chapters are different stories with different narrators it's all, as Ai says, "one story" (1.2).
This actually connects to the idea that Ai's name sounds the same as the "I" of the first-person narrator. Le Guin toys a bit with our expectations here. Generally, we think of the "I" as being the only teller of the story, but Le Guin is saying this "I" —that is Ai—is not a single person. Rather, he is the "I" of all these stories coming together to create a single tale. We have more on this admittedly mind-boggling idea in Ai's "Character Analysis."
Okay, time for a break.