How does someone Strike an object by RAW? Page 272 makes intimations of such a thing, and page 515 backs this up. Indeed, page 515 actually makes it terribly easy for a 1st-level character with a two-handed weapon to break down a hewn stone wall over the course of several rounds (especially a Power Attack fighter), provided that it is not "well-maintained."
But how does the process work mechanically? As per page 471, Strike says, "You attack with a weapon you’re wielding or with an unarmed attack, targeting one creature within your reach (for a melee attack) or within range (for a ranged attack). Roll the attack roll for the weapon or unarmed attack you are using, and compare the result to the target creature’s AC to determine the effect. See Attack Rolls on page 446 and Damage on page 450 for details on calculating your attack and damage rolls."
Objects are not creatures though, and objects do not even seem to have AC. Is this an error? Is it supposed to say "creature or unattended object"?
Specific > general
You Strike and damage the object, it doesn’t have AC but then there’s this
Strong walls, such as well-maintained masonry or hewn stone, can't be broken without dedicated work and proper tools. Getting through such walls requires downtime.
There's also the Athletics action:
Force Open Single ActionAttack
Source Core Rulebook pg. 242
Using your body, a lever, or some other tool, you attempt to forcefully open a door, window, container or heavy gate. With a high enough result, you can even smash through walls. Without a crowbar, prying something open takes a –2 item penalty to the Athletics check to Force Open.
Critical Success You open the door, window, container, or gate and can avoid damaging it in the process.
Success You break the door, window, container, or gate open, and the door, window, container, or gate gains the broken condition. If it’s especially sturdy, the GM might have it take damage but not be broken.
Critical Failure Your attempt jams the door, window, container, or gate shut, imposing a –2 circumstance penalty on future attempts to Force it Open.
You can strike any unattended object you like, but you cannot strike an attended one.
It's as simple as that.
You probably won't have to roll to hit the object, unless the GM says it has an AC for whatever reason.
The damage it takes is whatever damage you do, minus the object's hardness.
As per the rules (p272).
"Item Damage: Normally an item takes damage only when a creature is directly attacking it—commonly targeted items include doors and traps. A creature that attacks you doesn’t normally damage your armor or other gear, even if it hits you. However, the Shield Block reaction can cause your shield to take damage".
The 'sabotage' Rogue feat changes this a bit: you can attempt to damage an attended object as long as it has movable parts (eg: bow = yes, sword = no).
Oh, Ok. I thought you could target a weapon or armor like the old sunder. Sad. It would have allowed me and my players other ways to go about fights. Maybe focusing down big bads full plate in the first couple rounds to make the other rounds easier. Oh well.