What are the specific mechanics governing how shields work in Breath of the Wild?

I don't mean, "what button activates them," or anything like that. I'm trying to understand how shields function as a defense mechanism in The Legend of Zelda: Breath of the Wild. Here's what a (partially made up) version might be for how armor works:

Armor reduces the damage Link takes. Each piece of armor has a protection rating, and the pieces you equip (up to three) are summed up to generate the total protection. Each point reduces the damage taken by a quarter heart, with the caveat that any hit will cause at least a quarter heart of damage. (So, a four armor rating will reduce a three-heart hit to cause two hearts damage, and cause a one-heart hit to cause a quarter-heart damage.)

(Hat tip to @Fungo for helping me improve my example there.)

With a shield, I really don't know how it works:

• Does it repel some attacks, based on rating, and those it doesn't repel hurt the same? Or does it reduce the damage from all, and some are reduced so much that they cause none (and appear repelled).
• And how does it get used up by that mechanic? Is it worn down "once per use" like weapons mostly are? Or is a successful use "absorbing" some amount of damage, so it can be used many times agains a weak attack or once against stronger ones?

Firstly, a shield will block 100% of incoming damage. The shield may break, but you won't take damage if you're blocking.

This thread sums up a lot of how shields work quite well.

So what does it mean and why should you go for higher numbers in the first place? They all block 100% of the damage, so why not just aim for high durability shields? Simply put, shields with higher numbers will interrupt more attacks and throw enemies off balance more often by simply blocking compared to shields with lower numbers.

Here's an example to help illustrate this: Bokoblins can perform a three-hit combo. If you block with a pot lid, they'll perform all three attacks before returning to their combat stance as if nothing happened. If you block with a strong shield instead, they'll do the first hit then immediately get thrown off balance and become vulnerable.

As for how damage is applied to the shield itself and how it affects durability, this page explains what does and doesn't hurt your shield. Essentially, blocking (but not perfect guarding -- this doesn't lower a shields' durability at all) and surfing on rough terrain are what lowers the durability of shields.

Soaking the enemy's attack on your shield will eat away at its durability. ... Be extra careful against Guardians. If their beam hits your shield on a normal block, it's going to be destroyed. Almost all shields break in one beam, Royals in two.

While not explicitly stated here, it looks like stronger attacks will eat up more durability, which would explain why guardian lasers are so devastating to shields.

As for how surfing affects your shield's durability:

Surfing in the sand or snow? Great! Hardly a scratch. Surfing down a rocky cliff? That's going to cost you. The type of terrain you choose to try to surf on will cause different amounts of durability loss to your precious shield. Grass is pretty easy on the shield, but the actual landing from when you impact your shield on the ground is going to take a little bit extra out of the shield each time you jump. Overall, though, just avoid trying to shield surf along those abrasive rock surfaces.