WARNING: There are going to be SPOILERS in this post, if you haven’t seen the finale.
I have a hypothesis about how Amon was able to take away bending. I think he used blood-bending to block your chi. The chi-blockers hit your pressure points to temporarily block your chi, which makes it so you can’t bend. Amon probably adapted this technique, but uses blood-bending to make it more permanent. You can use blood-bending to break an arm, so you can probably “break” those pressure points, I guess. (This still doesn’t really explain how Katara couldn’t figure out how to reverse it, but I guess she wasn’t practiced enough with blood-bending.)
What Amon does is different from Aang because I think Aang is actually bending your chi. Chi is basically spiritual energy, so it jibes with what the turtle island was saying about this technique. Summarized: Aang bends chi; Amon blocks chi.
I think this also explains why Korra was able to air-bend. Amon blocked her chi for all fire-bending, water-bending, and earth-bending. But he didn’t block it for air-bending. So, when Korra tried to bend, all her chi was directed into air-bending. It’s as if water was pouring out of several spigots and then forced into just one.
I’m guessing Amon never really knew how to block airbending and may have failed with Tenzen too.
None of this explained how she got her spiritual powers so fast at the end. In general, I’ve been pleased with the pacing (others will disagree) of the show, but I thought everything resolved itself way too quickly at the end. (Tarlock loses his powers way too fast, and then it’s a whirlwind from there.) In fact, I’m disappointed the season didn’t end on a cliffhanger.