One mechanic for every tameTaming: boars, wolves, lox and the rest
30 minutes of fed, calm time to reach 100%Every tame works the same way underneath: the creature has to eat food you drop while calm, and eating fills an invisible acclimatization bar that takes 30 minutes of fed, unbothered time to reach 100%. Hover the creature to see the percentage tick up. Anything that scares it (you standing too close early on, nearby enemies, taking damage) pauses the process, so the whole craft of taming is arranging peace and quiet.
Build an enclosure, get the creature inside, throw a stack of its food over the fence and walk away out of sight. Come back to top up the food every few minutes; a fed tame stays fed for 10 minutes at a time. Yellow hearts mean it is eating and taming, and once tamed you will see a name-tag heart when it is happy. A Brew of Animal Whispers doubles taming speed if you want the 30 minutes down to 15. The devcommands cheat tame exists when you just want to test a build.

Boar
Build a small pen, lure one in by standing inside until it charges, then hop the fence and toss food over. Two fed, happy boars breed piggies. The classic first farm: leather scraps and meat forever.

Wolf
The only commandable tame: follow, stay, and guard. Night-spawned wolves despawn at dawn unless already tamed, so pen a day-spawned one or keep the night wolf eating until the bar fills. Breeds like boars. Cubs never flee, which is why breeders keep the cubs and release the parents.

Lox
Too big for fences: trap one in a stone pit or simply feed it in the open, it will not wander far while eating. Fed lox produce calves. A bred lox herd flattens fuling raids on its own.

Hen
Buy the first egg from Hildir for 1,500 coins and keep it warm next to a fire until it hatches. Hatched hens are already tame. Fed hens lay eggs that hatch near warmth. One egg from Hildir becomes an infinite chicken farm.

Asksvin
Steal an egg from an asksvin nest or tame an adult; they hit hard, so trap them in ruins rather than wooden pens. Pairs lay eggs like hens. Bred asksvin are the Ashlands cavalry and a top-tier mount.

Moose
Lingonberries are the only thing a moose will eat, so the whole tame is one berry run. A Moose Saddle (Black Forge level 2: 4 bloodgold, 5 seal pelt, 5 timberwood, 15 linen thread) makes it the fastest mount in the game at 12.6 run speed, against the asksvin's 9 and the lox's 7. Fed pairs drop calves, so hide, sinew and meat come out of a pen instead of a hunt across the ice.
Skelett is the odd one out: it is not tamed with food at all, it comes already loyal when summoned with a Dead Raiser staff.
If the bar refuses to move, something keeps spooking the animal. The usual suspects: you are inside the pen with it, a greydwarf is poking it through the fence, or it is a night-spawned wolf that will vanish at sunrise. If a tame starves it does not un-tame, it just will not breed, so breeding pauses are almost always a food problem. And tames can die: keep boars out of boss fights and wolves away from deathsquitos unless you have bred a two-star army that can take it.