Third Person Omniscient
We almost wish there was a new word to describe the point of view for The Hitchhiker's Guide, something like talky-omniscient (because the narrator tells us so much) or joke-niscient (because the narrator tells us so many funny stories).
Usually, an omniscient narrator can jump into people's heads and tell us what people are feeling, and we get a lot of that here. Even minor characters like Prostetnic Vogon Jeltz gets this treatment; so, for instance, instead of the narrator telling us that Jeltz looks mad, we get this: "He always felt vaguely irritable after demolishing populated planets" (5.38). This narrator will dip into everyone's head (even both of Zaphod's) to tell us what they are thinking and feeling.
Omniscience is useful because it can show us all these feelings and tell us other things that we need to know to understand the story. For instance, the omniscient narrator in Uncle Tom's Cabin can tell us about slavery, and the omniscient narrator in Moby-Dick can tell us about whale hunting. In the same way, the omniscient narrator here can interrupt the action to tell us about the Infinite Improbability Drive (10), or about the Magrathea entry in the Guide (15), or about how Arthur's comment about "lifestyle" sparked a war (31.2).
Now, only two of those three stories actually affect the action in this novel. The third story relies on something Arthur says, but it never affects what happens in this book. The narrator seems to include this story just because it's a funny story he wanted to tell us. The narrator is almost a character himself, in a way, since he's not just telling the story and getting all up in the other characters' heads; he's also having a good time joking around with us.