This blog is probably Part 1 of multiple parts, as I'm still learning the new edition, but here are a few things that weren't immediately obvious to me:

1) Touch spells don't require an attack roll unless they say so. In First Edition, any spell with a Range of "touch" required you make a touch attack roll against your foe to hit it. That's not the case now. Now, plenty of spells have a Range of "touch" but don't require any attack roll. The spell text says if it does. For example, chill touch and purple worm sting don't require attack rolls, but shocking grasp does. 

2) Critical hits automatically double. When you critically hit with a weapon in First Edition (and most other RPGs I play), you scoop up twice the normal amount of dice and roll them. Instead of 1d8+4, you roll 2d8+8. Not anymore! Now, you just double your roll (although the GM might permit the "old way"). So 1d8+4, then double the result.

3) Nonlethal damage is much harder to pull off. In First Edition, you could deal a special category of damage to foes, called nonlethal damage or subdual damage. Doing so even early in the fight made it a lot more likely you could knock out, rather than kill, your foe at the end of battle. To be honest, I like the simplicity of a system that is "whoever lands the blow that took a foe to 0 HP decides whether the hit killed or knocked out the enemy," but that's not Pathfinder Second Edition. In 2E, you take a -2 penalty to make your strike a knockout blow (rather than -4, in the old system), but it only matters if your strike is the last hit that takes your enemy down. If that last blow was a nonlethal blow, the foe is unconscious; if not, the foe is dead. Most players don't know when that last blow is, however, as most GMs keep monster Hit Points secret! So if you want to take a prisoner rather than just kill your foe, you should be taking this -2 penalty all the time. And even then, your Chaotic Neutral rogue buddy, who isn't taking the penalty, might just sneak in that last blow and your foe is dead anyway. 

4) Critical hits don't need to be confirmed. Like other games, a roll of a 20 (or a very high roll against a very easy foe) is a critical hit. No need to "confirm" the attack roll by rolling it again, like in First Edition. This roll-to-confirm structure has fallen out of use in a other games, too, so I suspect that years from now, players of First Edition will roll a 20, be happy to see it, then have to back up and say, "oh, wait, I have to do another thing before doubling my damage. Wait, I don't just double it, I roll the dice twice? Huh, weird." 

Enjoy the game!