I’m going through the rules and while most of them are pretty simple and easy to understand I just can’t get a grip on armor piercing and how to figure it in.

I understand DR so lets assume I hit a monster in the chest with nothing blocking the shot.  The shot came from a gun with a damage of 3d4 with armor piercing rounds.

So to determine damage I would look at the monsters Defense rating (lets assume a rockscythe) so that would be 10 and his armor for high velocity kinetic is 3.

Where does the armor piercing rounds come in at and what would they do?

Quite simply, any AP ammo bypasses a certain amount of Damage Threshold/Resistance.
So for your example, let’s say that the shot came from a gun doing 3d4 damage with AP 2 (the standard AP for AP ammo per 9.5.6 of CRB).
The damage roll for the 3d4 rolls max damage of 12 points.
Under normal circumstances, the Rockscythe would take only 9 points of damage. 12 points - 3 for HVK Damage Threshold = 9.
However, since the ammo is 2AP, it ignores the first 2 points of the Damage Threshold, so the Rockscythe takes 12 - 1 = 11 points of damage.

There is a good example of this in the core book under 7.11.7

Thank you Kane ... I was making it harder than it had to be.  Probably hopped up on too much caffeine or something.  lol

No problem, but I failed to mention one thing. AP ammo bypasses a certain amount of both Damage Threshold AND Damage Resistance.
So AP ammo could bypass (ignore) 2 points of Damage Threshold and 2 points of Damage Resistance, thus technically being 4 points more effective than standard ammo.

That makes perfect sense.  Thanks again Kane, appreciate it.

Glad I could help clarify that for you.