Rounds and initiative
When a fight breaks out, time slows down into rounds. A round is about six seconds, and in it every creature gets a turn. The order is set once, at the start, by an initiative roll — usually Perception, sometimes a skill if you were doing something clever when things kicked off. Highest goes first, and that order holds for the rest of the fight.
On your turn, you act. Between your turns, you watch for your moment — because you're never fully idle, even when it isn't your go.
Three actions
This is the heart of combat, and it's beautifully simple: you get three actions on your turn, and you can spend them on almost anything.
Step, Stride, Strike. Draw a weapon, raise a shield, open a door, drink a potion, cast a spell. Most things cost one action; some cost two or three. You spend them in any order, mix and match, and you don't have to use all three — though you usually will.
Three Strides to close the distance. A Stride and two Strikes. A spell that eats two actions and a step to safety with the third. The turn is yours to build.
Attacking
A is the classic attack: roll a d20, add your attack bonus, and compare it to the target's Armor Class (AC). Meet it or beat it and you hit; beat it by 10 and you crit, dealing double damage. Then you roll the weapon's damage and add it on.
Here's the one rule that shapes every fight: the multiple attack penalty. Your first Strike each turn is at full strength. Your second takes a −5, and your third a −10. (Lighter, agile weapons soften that to −4 and −8.) That's why three wild swings is rarely the best turn — the third one usually whiffs. Often you're better off doing something else with that last action.
Taking damage and dying
Damage comes off your Hit Points. Run out and you fall — but in Pathfinder, falling isn't the end. You drop unconscious with dying 1 (or dying 2 if a critical hit put you down). At the start of each of your turns you make a recovery check: a flat check against DC 10 + your dying value. Beat it and dying drops by 1; crit it and it drops by 2; fail and it rises, climbing faster on a critical failure. Reach dying 4 and your character dies.
Being healed to 1 or more Hit Points clears dying, but leaves you wounded 1 — and wounded adds to the dying value the next time you go down, so each trip to the floor is more dangerous than the last. That's why you don't let a downed ally lie there: getting them up, even to a single Hit Point, pulls them back from the edge before the math turns against them.
Reactions and free actions
Your three actions are only part of the story. You also get one reaction each round — a single response you can trigger even when it isn't your turn. A fighter might strike an enemy that drops its guard; a shield-bearer might block a blow as it lands. Reactions have a trigger, and when it happens, you choose whether to spend yours.
Free actions cost nothing at all — a shouted word, a simple gesture, releasing something you held. Use them freely, as the name promises.
Learning to hold a reaction for the right moment is one of the quiet skills of good play. It's the difference between a turn that ends when you say "done" and a character who's dangerous all the way around the table.