When determining starting age randomly (see “Age” section in the PRD or d20PFSRD), how do you know which of the Intuitive, Self-Taught, or Trained categories a hybrid class counts as? Specifically I'm wondering about Arcanists, but I want to know the general rule too.
The rule is this: If there's a line somewhere that specifies a particular class counts as Intuitive, Self-Taught, or Trained for the purposes of generating random starting ages, it uses that column of the table.
If you find a class and can't find anything that specifies which column of the random starting ages table it should use, you (or your GM) will just have to make a ruling about which column is appropriate - probably by comparing the flavour of how members of the class gain their class abilities to that of other classes. ("Intuitive" classes seem to be those flavoured as being learned at the school of hard knocks, "Trained" classes seem to be those flavoured as requiring a whole lot of book learnin' or ancient and mysterious oral lore, and "Self-taught" classes include everything else.)
In my personal experience, very few Pathfinder campaigns last long enough for age to have any meaningful mechanical effect; Experience points are gained rapidly enough that few characters see more than one age category before retirement. Under such conditions, generating age randomly is just a different way of pulling a meaningless number out of the air. I therefore recommend you don't stress too much about random starting ages.