I recently learned how the Spartans would annually declare war on the Helots so I was wondering how exactly would said "war" proceed? Would it be essentially like releasing a fox in a chicken coop or would it be more like a farmer choosing which animals to slaughter?

I've made a couple posts about this that I will try to dig up, but put broadly our actual, concrete knowledge of Spartan society is extremely ephemeral. Lots of people wrote down stuff about Sparta, but for one reason or another the great majority of it is pretty unreliable. Most of the more lurid details, for example, come from the author Plutarch, who wrote down quite a lot about Spartan society...in the second century CE, about half a millennium after what he describes and, more importantly, after Spartan society had been flanderized, so to speak. By the Roman period, "Sparta" had already become heavily idealized as a society in philosophical thought and literature. The roots of this can absolutely be seen in the classical period, with people praising Spartan laws and the like, but it got kicked into overdrive, so to speak, during the Hellenistic, particularly under king Cleomenes III, who embarked on a program to revive ancient Spartan virtue and glory, which he saw as being tainted by recent history. As we well know, programs of reviving past virtue tend to be a lot more extreme than anything that existed in the past. Then after the Roman conquest, Sparta lost its civic power and became a sort of tourist destination, thus making the stereotyping even more extreme. And then adding still more, Plutarch himself is not exactly averse to his own stereotyping.

And so when we get down to what we actually have from sources of the period, it is a much smaller list. To give an example, in contemporary sources like Xenophon or Herodotus there will be casual mentions of entire social classes like the perioikoi (lit. "those who dwell around") and the skiritae that aren't described in the later, more detailed sources and so who we really don't know anything about. What we can say for certain, though, is that actual classical Spartan society was far more complex and far less stereotypical than its later portrayals.

As for the krypteia (the terrorizing of the helot populations), the best explanation I have seen argues that it wasn't some sort of hellish, general genocidal program (albeit it was obviously pretty brutal), but rather it was a specific program to counter the specific problem of helot unrest. Most explanations I have seen recently argue that it was some sort of quasi-professional counter-guerrilla force. They would obviously employ brutality, but it wasn't for the purpose of creating an citizenry of unthinking monsters, as Plutarch portrays it (although e is a bit more positive about it), it was to stop helot unrest.

I was looking around for the particular Paul Cartledge article about it and stumbled on this free to view piece that covers the topic quite nicely, I think.