I wrote this in response to a question about coming to Pathfinder 2e from D&D 5E…, and was pretty happy with it, so I'm capturing it here for reference.
Hello all, I'm getting ready to run my first game of Pathfinder 2e but have limited knowledge of how the game is actually played. I have been a big 5e player and learned to DM for 5e from Matt Colville's "Running the game" series. […]
PF2E is run like any D20 system, so watch your favorite D&D AP and you get the idea. And while it is fundamentally a tactical combat game, that means it /can/ be run like your favorite actual play, so if you want something more role-play or narratively driven, or something more mechanically focused, you can do it in that way. Maps and minis (real or virtual) sure, but I've done and listened to plenty of really great theater-of-the-mind D&D 5E and PF2E combat, and plenty of amazing hours with not a single combat die rolled.
Mechanically, of course, PF2E has some distinct things:
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The 3-Action economy, of course, but this is ante to the table…
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DC-by-level is a good thing to understand to get at the core of the system's math. They don't state it, but from levels 1-20, the formula is "14 + ${level} + floor(${level}/3)", and level 20+ it's (2×${level}).
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Natural 1s and natural 20s aren't necessarily a crit, they adjust the degree of success by one level. So a natural 20 (plus eg. 5, for a 25) is not a crit against an AC (DC) of 26, but it does turn the fail (25 < 26) into a success. A nat 1 (plus eg. 6 for a 7) is not a crit fail against a DC of 6, but it does turn the success into a failure. Similarly, really (bad/)good roll that's /not/ a natural (1/)20 might be a critical (fail/)success if it's 10 (below/)above the DC. Natural 18 plus eg. 8 for a 26 against an AC of 16 is a critical hit.
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"±1's matter", and Mathfinder is still Mathfinder, so making sure things are accounted for is important. Foundry is great, if you're into that.
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Characters are a "bag of feats", so your players really need to know their character and remember when they have relevant feats to apply to a situation. I personally like to create my own sort of "playbook" for my characters that reminds me of feat-effect + action combos to take in various situations.
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Related to the previous, multi-classing does not exist in the same way. See Archetypes and Dedications, which are a PF2E's approach to the idea. Look at the very popular "Free Archetype" variant rule, which allows character breadth and options without breaking character power (due to the action economy being the fundamental restriction on power (creep)).
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Conditions and persistent damage work a bit differently, so review that. It's important to respect how they work in this system so creature abilities don't get out of balance.
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Casting works a /little/ differently (concentration, heightening, slots, prepared vs. spontaneous) so again respect the system and its balance. See the Flexible Spellcaster archetype to understand how PF2E implements a 5E-like casting approach; even if you don't use it, it helps map the concepts across the two systems.
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Victory Point systems are Good, so use them when relevant.
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Recall Knowledge is a bit amorphous, so spend some time understanding what it can('t)/should(n't) provide.
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Hero Points are the meta-currency here, so do that, and tweak/house-rule as you see fit.
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Internalizing Automatic Bonus Progression will help you understand the core system math and expectations across levels — even/especially if you don't use the rule and want to give out items as is traditional)
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Internalizing Treasure by Level will help you understand how to dole out loot (see previous).
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Internalizing the Encounter Building Rules is important, since things work differently (and better) than 5E.
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Look outside of d20 systems for other inspiration on being a good GM. PbtA-and-derived systems have great ideas that will make you a better d20 GM. Groking the concepts of "success at a cost" and "fail forward" (you don't succeed, but still advance (slowly) toward the goal) are key, and will help you characterize rolls better.