Does Mr. Vinge ever mention how the Zones work in his Zones of Thought series? I know that the book mentions that they may or may not have been created by a higher power, and that they are shrinking and may exist in other galaxies, but how do they work?
Based on my shaky recall of all 3 books and the first short-story The Blabber, it's not explained.
I guess you're referring to the hint in A Fire Upon the Deep that "There are Things that don't like the Blight" and "Maybe there are Cloud People". You're probably are aware of the speculated reason for them: so that lesser lifeforms are able to develop, without being immediately destroyed by greater beings - a protective barrier. It's a nice theological creation story, these Cloud People being Powers (Gods) beyond the Powers. I'm not sure where this is, but maybe early on, in the speech Ravna gives on her date with Pham, explaining the Zones to by analogy with "deep" waters. Or perhaps it was near the end, along with the two quotes above.
But I don't believe he ever even hints at "how they work"!
He does mention their qualities: faster than light travel; even faster messages; and sapient machinery (but we have sapient machinery already - us - so why does that need a special zone?). I don't think he says it, but I have a feeling it may be to do with NP=P in higher zones, but not down here.
BTW: Of course he has stated the literary reason (in the intro to the The Blabber, and elsewhere too, I'm sure): he believes in the Singularity, and that it would make a boring and unrelateable world to write about, coming in the near future. Therefore, he invented the zones so the future could still be relateable. The Beyond/Transcend corresponds to what would happen in the Singularity, and he carefully does not give any detail about it. The characters in the stories speak of inhabitants of the Beyond as we would speak of gods.
Hmmm... It's probably a fair guess that there are two concepts wrapped up in the Zones - one is to stop the Singularity so there's a limit on technology; the other is to allow ftl travel, as many scifi writers do (when I think about it, ftl also acts to make it relatable: ftl makes worlds like continents, space like the sea, spaceships like ships; faster but bandwidth-limited communications give usenet-like messages).
The zones are regions of space where it is possible to utilize a level of technology. Faster zones are more advanced up to a point where the singularity is achievable.
In one of the books its said that the zones shift but why and how is not explained.
It is hinted that the habitants of the higher zones (Powers and cloud people) are able to cause the shift of the zones and Pham used the Countermeasure to trap the Blight in a slow zone.
Vernor Vinge doesn't explain the mechanics of how the Zones work, but he does give some clues as to their basic physics. He mentions that the Zones correspond to galactic mean density, so that their nature - the ability of each individual Zone to allow or sustain a certain level of intelligence or technology - may be correlated to the amount of relative mass there. This would also correspond to the relative amount of gravitational energy in the different Zones; this gravitational energy may be what dictates the upper limit on technology and intelligence between and even within the Zones (as in the vast differences in FTL potential between the Bottom, Middle, and Top of the Beyond). It also explains why the Zones are shrinking, as the matter within galaxies is pulled toward a common center of mass, perhaps a supermassive black hole in the Unthinking Depths.
So it may be that Powers beyond the Powers that Pham experiences when running the Countermeasure exist and operate in a region (relatively) free of interference from mass and gravitational pull. What their interest is in the Unthinking Depths is unclear, though the Powers in the Transcend are also interested.
The OnOff star is such a curious object that one is led to suspect it may have something to do with the zones. A defective mechanism, perhaps?
It's pretty much stated outright that a power a very long time ago recognised the problem - higher powers stompinng new civs before they get a chance - and engineered a solution that persists, and has been resilient against all later powers.
Those capabilities are far beyond anything demonstrated by anyone in the stories.