Armor comes in three approximate types:
Armor of different types almost always stacks.
If the character has more than one piece of armor for a particular type, they receive the best melee rating and the best ranged rating from the armors they're wearing. If any piece of armor has the Bulletproof advantage, the character gains its benefits, even if the armor's ratings are overshadowed by another piece of armor.
The penalties from every piece of armor also stack.
For example, Goban is about to enter combat. He has studied the Aggressive Unarmed Strikes style, so he gains the technique's 1/1 armor vs bashing. That's his only Inherent armor. He is wearing a suit of hedgespun leather armor, which provides a 3/2 rating, over a low-profile bulletproof vest, which grants 0/1 and is bulletproof. These combine, providing a Worn armor bonus of 3/2 from the hedgespun and bulletproof from the low-profile vest. Just before entering the fray, he activates Elements (Metal) 2, which grants 1/1 for his External armor. Having armor of all three types means we have to add them up for his final armor rating: 1/1, 3/2, and 1/1 sum to 5/4 Bulletproof against Bashing attacks, and 4/3 Bulletproof against everything else.
For most games, bulletproof armor is always considered to include trauma plates unless explicitly noted otherwise. These add extra protection for the torso, allowing the armor to retain the bulletproof advantage against ranged weapons whose damage code surpasses the armor's rating. However, bulletproof armor is soft everywhere else. Weapons whose behavior depends on 'hard' vs 'soft' armor (like broad head arrows) may treat targeted attacks against limbs as 'soft' even when the target is wearing bulletproof armor. For simplicity, this does not affect the bulletproof advantage.
More detailed rules for bulletproof armor can be used if desired.
Armors that rely on a certain type of damage must be compared against the innate damage of the weapon before modifications.
For example, a thick padded coat might grant 1/1 armor against Bashing attacks, so things like fists and bats would be penalized by -1. Knives and bullets would not suffer any penalty, since they deal Lethal damage natively. Putting a thin bulletproof vest underneath adds the bulletproof quality, which downgrades incoming firearm damage from Lethal to Bashing. However, the gun still does Lethal damage natively, so the bulletproof vest does not allow the padded coat to penalize firearm attacks.
Inherent armor most commonly comes from the Aggressive Striking fighting style or one of its related styles, which grants 1/1 armor against Bashing damage only.
Likely the most powerful inherent armor is obtained through the fifth clause of the Contracts of Stone, which grants 1/1 armor against all incoming damage for every success on its activation roll.
Worn armor is easy to come by. Football padding provides 1/1 armor, as does a leather coat or any other thick, resilient clothing.
Anyone who wants serious protection wears more serious body armor, which in today's world means it's bulletproof. Bulletproof vests, flak jackets, Kevlar shirts, riot gear, and so on provide different levels of worn armor against all threats. See the Armory book for details.
External armor is extremely rare and can only come from magic. Elements 2 provides armor 1/1 of the appropriate element, for example.
Another form comes from Summer Mantle 3, which grants 1/1 armor against all incoming damage.
When it comes to fire, it really helps to have more than one layer of armor. Each source of armor applies its full melee rating against the flames for as long as it holds out (see World of Darkness p. 180). Any damage which overcomes the first layer affects the second layer instead of being applied directly to the character's health.
When armor granted by contracts doesn't have a Structure rating, it lasts a number of turns equal to half the Changeling's Wyrd, rounded up.