Here's an example with some characters from my game:
Doc, a Hermetic Mage, is on his way to the Stuffer Shack for some Queso Soyritos, a can of Fizzy Goop, and a box of gauze to patch up his team's Face. On his way there, he is accosted by FailBoy, a ganger who has picked on the wrong random passer-by. One thing leads to another, and FailBoy pulls a gun. Doc takes exception to that, and slams him with an Ice Spear.
Doc casts a Force 7 Ice Spear, and gets 5 hits on casting. (And rolls his Logic + WIllpower to successfully resist (Force-3) 4S Drain)
FailBoy must be a little hungover tonight, and only rolls 2 hits defending against the Ice Spear.
Now FailBoy must resist 10P (Force 7 + 3 net hits) Cold damage, using 9 dice (Body 4 + [12 Armor Jacket - 7 AP]). He gets 3 hits, and takes 7 boxes of damage. Since the damage is higher than his modified armor of 5, it is Physical (ouch!). He's also knocked down, since the 7 damage he took is higher than his Physical Limit of 6.
Now, he needs to need to roll dice for his Armor jacket equal to it's armor value of 12. If he gets no hits, the object breaks and needs to be repaired. If he Glitches, it breaks and can't be repaired. If he Critically Glitches, it breaks in a way that is dangerous.
FailBoy is now on his back, with 7/10 boxes of Physical damage, and it's possible (but unlikely) that his Armor Jacket is no longer providing him with armor. He begins to reevaluate his life choices.
As for armor stack items and 'ware, I mostly agree with jim1701. I wouldn't make them do it for cyberware, and depending on the situation I might do it with helmets, forearm guards, etc. The rules don't directly address either situation, however, so it's going to boil down to what the GM feels like doing.