Could someone go over armor again...I tried the quick start rules and those were not very clear, I looked into the book and I think I got it but I'm still a little confused about how AP and BAR work....
The Quick start rules are simplified for you to get an idea of the game, and so is combat (and AP and BAR are simplified).
Page 15, in the upper right, has an example of how things work between AP and BAR for the Quick Strike rules (Keep in mind, the main game has many advanced rules such as specific body locations (and damage to them), bleeding, critical hits, etc. etc.)
For Quick Strike, you simply subtract the AP from BAR. Negatives are treated as 0. If the number is positive, subtract that number from the weapon's damage. So, for example:
Character A, with a knife (AP 1), attacks Character B who has body armour (BAR 2 - A Cooling Vest let's say): 2 (BAR) - 1 (AP) = 1 damage mitigated. If the Knife attack is dealing 3 damage*, we subtract the 1 that the armour absorbed to get 2 Damage total dealt to Character B, which automatically includes 1 Fatigue as well.
So Character B is stunned (automatic from taking damage). He shakes it off with a simple action, then spends his other simple action firing back with a M & G Service Auto Pistol: 3 / 4 ( AP / BD). Let's assume it hits. Let's assume Character A also has a Cooling Vest on (BAR 2). So we subtract the 3 (AP) from the 2 (BAR): 2 - 3 = -1. The vest doesn't mitigate any damage (we treat it as 0). 4 (BD) - 0 = 4 Damage dealt. We get 1 Fatigue and stun applied automatically.
If Character A, however, is wearing a Flak Vest (BAR 5) the damage would be reduced by 2 ( 5 - 3 = 2), resulting in 2 total damage (4 BD - 2 = 2). Or, if Heaven help Character B, Character A is in a heavy Body Armour suit (8 BAR): 8 - 3 = 5 which reduces the damage to 0: (4 BD - 5 = -1 = 0 damage). When no damage is dealt, there's no fatigue and no stun effect applied.
* - Melee attacks, such as knives, add strength/4 (rounded up) to the melee weapon's damage. So someone with Strength 5 would deal 3 damage with a Knife (1 BD) because 5/4 = 1.25 rounds up to 2, which gets added to the 1 BD of the knife for a total of 3 damage