There was some confusion over this in my group. We've probably just gone dumb and blind and can't find out, but a concrete answer from someone here would really be appreciated.
The rule you're looking for is on the first page of the skill chapter, during the introductory section. Much like 3.5's wealth-by-class table, being in the introductory page means it's often missed, but it's there.
It says something like "All adventurers have basic competence in all skills"
Yes, adventurers pick up bits and pieces of this and that as they level, as they accumulate experience. Makes sense really, although you can do extra stuff if you Train in a skill.
Yes, you can use any skill. But the are some uses of certain skills that require you to be trained to attempt.
Such as Arcana's Detect Magic use. Only works for those trained in Arcana.