Here is a brief, obviously non-authoritative synopsis of my understanding:
One cannot be saved without being first called by God, that is, given the graces to approach the ordinary means of salvation: Baptism.
God desires all men to be saved, and gives each man sufficient grace to be saved.
God predestines no one to Hell, but there are those who reject Him, and who thus are damned through their rejection.
No one is saved without the merits that Christ won for the human race.
There are those who can be saved without actually being Catholic, but they must have invincible ignorance, that is: they must be absolutely ignorant of the grave need for them to become Catholic, and this ignorance cannot be one which they could have overcome.
Such individuals must cooperate with what graces God does give them, and they, like all others, must die with supernatural charity in their soul, infused there by God which led to perfect contrition for their sins, known to them by natural law, at the time of their death.
One must be very careful in overstating how common or uncommon invincible ignorance is. Frankly, we have no way of knowing, and we must do our best to evangelize everyone, and encourage them to become Catholic.
