Can someone please clarify page 2 of the Rules Reference under the "ATTACK" heading:

Each ship has the following standard critical effect: "[crit die]: if the defender is dealt at least one damage card by this attack, deal the first damage card face up."

If I resolve the critical hit die roll by turning a damage card face up, do I then deal another damage card face down to count as that critical hit's damage? Or do I count face up damage cards in my total damage when adding up total hull damage taken?

In one part of the rules it says that critical hits resolve a face up card, but ALSO count as damage too. I guess I'm just REALLY confused about the way critical damage is resolved so a really good explanation of that would be greatly appreciated! Thanks in advance!

The face up damage card still counts as damage. So if you succeed in making one crit hit the target's hull, it will recieve one face-up damage card, at which point it has one damage on it that has an critial (face-up) effect.

Check back to the Attack Procedure in the reference rules.

You calculate your damage total. Each Hit and Crit Symbol gives you one point of damage for this.
If at least one crit was rolled, you get to resolve a crit effect.
Unless you have an ability or upgrade card granting your ship crit effects, your only choice is the Standard crit effect.
Triggering a crit effect does not spend or use up anything from your damage total.

So, if you trigger the standard crit effect and your damage total ends up causing at least one damage card (rather than only shields reduction) then the effect is that the first of those damage cards is dealt face up rather than face down.

That's it.
Face Up Damage Card still counts as one damage.

Thanks!