As far as I know, the opposing pairs are as follows (Revan can correct me if I'm wrong):
Melee accuracy vs. melee dodge
Ranged accuracy vs. ranged dodge
Magic power vs. willpower
Magic accuracy vs. magic resistance
Stealth vs. perception
In some cases, a stat is used against a difficulty determined by the GM, rather than an existing characteristic of a living creature. For example, when trying to avoid boulders rolling towards you. But it works on the same principle, as far as I know. In other cases, new checks may be involved using existing characteristics. For example, a character with the second rank in one-handed weapons may make an accuracy check before dodging in melee combat and parry the opponent's attack.
That's how it works. I hope I haven't forgotten or confused anything.