I will generally be deciding that as we go along with the RP, but most non-combat dice rolls will be dex-based, with a few being dex/strength-based. 
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I think that's explained somewhere, anyways, weapons will also have damage values such as '1d6 + (stat modifiers)', where you'd roll a single six-sided die to determine extra damage. As for evasion/hitting, that's luck (evasion) vs. agility (accuracy). I think most of this is on the first post, under stats, but if it's not, then I'm sorry.